Batman/Gordon relationship in the movies (quick overview)

TIM BURTON MOVIES

As stated and showed many times on the site, the Tim Burton movies went back to the genesis of the mythology, to the roots of the franchise - Kane and Finger's original vision of the pre-Batman Detective Comics issues - before the editors ordered to brighten it all up and make it more accessible for younger audiences

Michael Uslan (producer): I only let Tim see the original year of the Bob Kane/Bill Finger run, up until the time that Robin was introduced (DVD) 

Commissioner Gordon appears in the very first panel in Batman's debut comic book appearance, Detective Comics #27. The first panel already tells us a lot. First of all, we find out that he's a good friend of Bruce Wayne. They're not too close but Bruce is shown to occasionally visit Gordon and Gordon often offers him to come along for the ride to the crime scenes.
  

This appears to be the way in the movie as well. We can see that Bruce Wayne was seated right next to Gordon,

and also his absence might have been ignored by the Commissioner considering that he thinks of Bruce as a bored millionaire even thought he likes him. Gordon is also invited to Bruce's fund-raising party.

Another thing that we find out from the very first panel is that he's unsure of Batman. At first he wants to arrest him

 "Hold it right there!"

but as Batman starts to deliver the criminals, he seems to accept his presence in Gotham. Gordon and Batman didn't meet and it was Batman who was communicating with him by sending him notes or occasionally calling him up leaving him a message with information on where to find the captured criminals, after which he would instantly hang up. All of his information on crimes and new cases he was finding out as Bruce Wayne while visiting Gordon in his office.
It is important to note that in the script Gordon was a cop on duty the day Waynes were killed, an idea used in Batman Begins. That's why Batman cared about Gordon and reacted when Bob the Goon took him hostage

In the 1989 movie, Gordon also receives a letter from Batman and the Bat Signal to call him in case of danger. The note is the only way they communicate together. In Batman Returns it seems like anyone can turn on the signal and Batman instantly arrives at the place of the crime, being alarmed by the signal looming in the sky. Gordon is seen talking to Batman but not with Batman. Batman ignores him and doesn't look at him, only giving him a quick reply  in the form of "We'll see" before leaving.

It's worth noting however that Gordon tried to stop the cops who started shooting at Batman at the rooftop and that according to the Batman Returns script he is hoping that Batman will forgive the city for buying into Penguin's scheme.

GORDON
Think he'll ever forgive us?

MAYOR
Probably not. But he'll always
help us.

Note that Gordon is asking the Mayor, not the other way around - yet another clue showing us that there's no real communication between Batman and Gordon

The original Gordon was very much a side character with a very small role, appearing only twice in the entire pre-Robin era (in DC #27 and in one panel of DC #28), and didn't return until DC #42.

JOEL SCHUMACHER MOVIES

In Joel Schumacher movies it is made pretty clear that Gordon and Bruce Wayne are good friends and know each other very well, judging by the conversation they have about Dick Grayson. Gordon of Joel Schumacher movies is the reflection of the Golden and Silver era comic counterpart, being a friend of Bruce and cooperating with Batman whenever possible, calling him either with a Bat signal (this time Batman comes directly to the source of the signal and talks to Gordon) or by video connection.

CHRISTOPHER NOLAN MOVIES

Christoper Nolan's Batman movies draw from the modern age (primarily Year One), in which Commissioner Gordon is a very important supporting character with a big role. The modern age showed Gordon and Batman having a trusty relationship and concern for each other, even thought on the surface they don't show it. There's clearly a mutual respect , trust and admiration, and Gordon could be perhaps included in Batman's "extended family" along Alfred. In both Batman Begins and The Dark Knight, Gordon not only provides Batman with important and valuable information but also directly takes part in the action, whether it's taking down a section of the bridge or capturing Joker.

Gary Oldman: You see a trust there when they're investigating ..when they're at a crime scene, you know, he will excuse his offices and his detective and give Batman the scene first. I know that for Batman Gordon is the only person that HE can trust, I mean other than [Alfred and Rachel] (Chuck Movie Guy int 2008)

It's also thanks to his support and push that Batman is ignored by the police and allowed on the crime scene.
While it's clear that Gordon and Batman have a personal friendship, they both rarely, if ever, step on a personal note, mainly due to Gordon's preference.

As the time goes by we see a major concern from Batman for Gordon when he gets a heart attack or when he's kidnapped by Joker when it's almost personal. It goes the other way when the news spread about Batman being brutally beaten by Bane. The same is shown in The Dark Knight when Gordon quickly rushes to help Batman after his fall with Two Face and is shown a genuine and deep concern for his state. They are also seen occasionally joking together, which further proves that despite what they themselves may admit to themselves and what may appear on the surface, there really is a friendship there.

Nolan's movies also show the trademark and common situation for the two when Batman is often seen disappearing before Gordon can finish the sentence...

...however it dropped the other trademark which is Gordon being started by the suddenly appearing Batman.

Another element that was dropped was Gordon's enormous smoking habit of which Batman was reminding him quite often and which later became a major plot point when Gordon had a heart attack and was then replaced by other detectives for some time.
In the Modern Age comics Gordon doesn't have any friendship or special camaraderie with Bruce Wayne and that also translated into the movie, which is the most evident in The Dark Knight in which Gordon refers to Bruce as Mr. Wayne and is never shown to be around him or talk to him otherwise throughout the two movies

Also, in Modern Age comics Gordon has an opportunity to shoot Batman when they first meet but he doesn't and Batman's speech is similar to the condensed "Now we're two".

Bane on paper and screen

COMIC BOOKS 

Bane's story begins long before he was even born. It begins with the introduction of a formula called Venom.

Venom was introduced in Legends of the Dark Knight #16 as a highly addictive, strength enhancing drug which could be taken either in pills or, in further stages of development, through injections and then directly into brain through surgery. After taking only one pill Batman's strength was boosted so much that he could easily lift the weight that has previously snapped his muscle.

After just weeks of taking the pills, he was able to take out a big thug with one hand who had previously beaten him up, and even rip a heater off the wall with his bare hands. The venom however, had profound impact on his psyche, and his behavior wasn't that far from the Joker's.

He repeatedly offended Alfred and even agreed to kill Gordon in order to get the pills.

After a month of isolation and pain, Batman gets off the pills and follows it's designers, Randolph Porter and his partner General Slaycroft to Santa Prisca. There, Porter performs further experiments with Venom on General's weak and thin son, Tim. Tim gets regular injections of a much stronger concentrate of Venom, and the eventually undergoes a surgery after which he turns into a giant bulletproof monster, a part of the venom  fed supersoldier squad

Slaycroft gets killed and Porter dies in a hospital from withdrawal from his own relaxing pills that he designed for himself. One could think that the formula died with Porter, however he did manage to record everything he knew on tape...

An unnamed child referred to as Nino was born in prison in Pena Duro, sentenced to life for his father's crimes. Nino was watched over by his innocent mother and raised as well as possible under the conditions, isolated form the rest of the prisoners. He was half Puerto Rican since his mother was a native and his father, as later revealed, was Batman's villain King Snake, most known from the first Robin series.

His story is told through the eyes of Zombie,  prisoner who was doing janitor service in Pena Duro and who watched over the boy whenever he could, watching him grow up. After his mother dies of sickness, Nino is placed among other criminals and it doesn't take long for others to harass him. One of the prisoners, Trogg, saves the child, but during a prison fight Nino falls over the railing and falls into coma. While in the coma, he has a vision and is visited by his future incarnation who tells him that if he will conquer fear, he can have anything. Note that when talking about fear, Nino sees a bat.

The child that wakes up after the coma is no longer Nino, and earns his name, Bane, the very same night he gets back to his cell by slicing his fellow prisoner to pieces.

For this and offending the Warden he is sent to isolation for years to die, but he survives and learns meditation and survival skills instead.

However, even in the isolation his dreams are haunted by bats

When he gets released, he is fearless and earns every prison fight, along with respect for surviving long years in isolation. His goal and obsession was to become what he saw in his dream, and he tirelessly honed his physical and mental skills. He was doing 1000 push ups and 1000 sit ups each day and read every book that was available in prison library. Learned many different skills from them and then he got Trogg, Zombie and Bird to smuggle him more books everytime new shipment for black market arrived.

Then, his life took another turn when Bird mentioned Gotham City and Batman. From this day, Bane's new obsession was born - to defeat Batman and rule Gotham. Even thought Bane didn't want to admit it to himself even, Batman was his biggest fear and became the main character of his nightmares, haunting his dreams every night.

After Bane kills 30 prisoners with his bare hands at once, he is yet again send to isolation, but gets out very soon to be a Guinea pig for certain experiments, with a new supersoldier formula that was created and based of Venom...

Bane as the only one survives days of injection treatment and then, as his last step of evolution, undergoes a surgery after which he looks exactly like he did in his epiphany. The surgery also implanted holes in his skull so he can feed his brain with venom directly.

Bane slows down his vital signs to the point where they become unreadable, and thus escapes Pena Duro. He goes back for Trogg, Zombie and Bird and the Warden who he then throws to sharks, but in the meantime kills a shark with his bare hands.

They then depart to Gotham where Zombie designs a device and mask which will allow Bane to pump venom into his brain and body at any given time. It was also Zombie who memorized the formula for Venom and was making it for Bane.

Bane tries to face Batman right away but quickly decides that in order to beat Batman, he must wear him out physically and psychologically, and must observe him and learn him thoroughly, and thus Knightfall begins. It is important to know that before he meets Batman, he gets very anxious and fearful, proving yet again that Batman is a personification of his fear

Bane observes Batman's action for months, and is shown to master almost every possible skill. Just by Batman's movement alone, he could tell that Batman is sick (he developed an Epstein-Barr syndrome) and could easily tell when Jean Paul Valley was in Batman's suit impersonating him.  Also, just by movement alone he could tell that Bruce Wayne is Batman

For months, Bane was aiding Batman's villains and observing the fight, sometimes even saving Batman's life. He was shown as a great tactical thinker and planner, and eventually decided and planned to release all the inmates of Arkham and armed them. Bane's sick obsession with Batman became evident even for his henchmen. He also wanted to face the physically challenging villains like Killer Croc himself, and he defeated Croc with ease breaking both of his arms. It's important to note that when Venom goes through Bane's body, he pumps up like a balloon

When the time has come, Bane faced the sick and weak batman and broke his back, confining him to a wheelchair for a long time, and taking over Gotham

Bane ruled Gotham for some time until the new Batman, Jean Paul Valley decided to take him down despite
Bruce Wayne's reservations.

Valley was a much more brutal Batman and much more armored and equipped. The first time he managed to hurt Bane but got pretty beaten up. The second time he went back for Bane was in full, newly designed armor. Combination of skills, equipment and Bane's weakness - which was an addiction to venom, contributed to Bane's fall.

Bane was placed in Blackgate prison and didn't return for a very long time, until Bruce Wayne returned as Batman, which fueled his fear and nightmares. It was yet another hint at Bane's telepathic skills. There was no way he or anyone for that matter could know that Bruce is ready to take the cape again.

In Blackgate Bane had to fight with the withdrawal from Venom. After he stabbed a prisoner in the eye he was sentenced to six months of isolation. That's where he fought his toughest battle yet

Getting off Venom had a profound effect on Bane. He was a changed man not only physically, but mentally as well. He no longer wanted to rule Gotham and no longer wanted to kill and hated Batman. He now realized that it was Venom who was poisoning his mind before.

He hates Venom now and wants to fight it and destroy it completely. Bane becomes an antihero. He breaks out of the prison and traces and fights off the gang who is distributing a drug that is derived from Venom. He actually teams up with Batman to get rid of the drug ring together

Bane even goes back to Santa Prisca to kill all the doctors that turned him into a Venom monster and destroys all the notes. For cleaning up the country from the drug, Bane is announced a National Hero.
After winning the war on Venom Bane becomes obsessed with finding his father's identity, but while on his search he meets and teams up with Ra's Al Ghul who choses Bane as the heir to his throne and a man for his daughter Talia

Bane comes back to Gotham and faces Batman one more time. This time however, the healthy and fit Batman wins the fight

The Bane and Ra's teamup didn't last long however, and very soon after it was Bane who was fighting against Ra's. Bane took out the entire League of Assasins and even went on a mission to destroy every one of the Lazarus pits.
Bane continued his quest in finding his father and then mistakenly thinks that Thomas Wayne was his father. He convinces Bruce about the fact and they both teamup again.
Soon after they both find out that Thomas Wayne wasn't Bane's father and Batman decides to help Bane in his continuous search. Bane's father is revealed to be King Snake, one of Batman's villains, but Bane doesn't switch sides this time around but instead saves Batman's life and helps him foil Snake's plans.

Bane soon joins a group of other antiheroes called Secret Six. While Bane fights thugs and bad guys and is off the Venom for so long, the one thing that didn't change is his temper and the use of extensive, gruesome violence. Bane has been shown to have a peculiar habit of ripping people's hands off and beating them up with them

Bane then went into a father/daughter relationship with a lesbian girl named Scandal Savage. She helped him out and showed a great care when Bane started having rough nights after a hunger for Venom returned. He was caring for Savage like for a daughter and would mercilessly kill anyone who would even look at her in a wrong way.

Even without venom Bane is always presented as an incredibly strong man, being able to kill large groups of armed men, break through walls and withstand bullet shots. In some ways he is even stronger because the addiction is gone. Being clean of Venom he defeated Azrael (Jean Paul Valley) very easily

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B A T M A N  &  R O B I N

Joel Schumacher: We use him in this film as Uma's pitbull, I mean she can't just kiss everyone to death in Gotham City, It's a lot of people to kiss and so sometimes she just needs someone to break down the wall (Anthology)

Bane was one of the three villains in Batman & Robin, although he was completely ignored by media. 'Three good guys seemed to mean three bad guys, including Mr. Freeze, Poison Ivy and virtually unpublicized Bane', once Batman's most merciless menace but here merely muscle for Ivy' (Batman: The Complete History). Few fans and most of the general public weren't even aware that Bane was going to be in the movie. Promotional posters were made for each hero and villain, but none for Bane. Bane was also almost never mentioned in the media and articles, which only talked about the movie having two villains, Mr. Freeze and Poison Ivy. However, Bane did have a separate photo session, in which he was photographed with Ivy and solo, and did appear on one promotional poster titled "Villains" which featured all 3 villains of Batman & Robin.

Most of the characters got changed or adjusted to the story during the translation from comic to screen in every movie featuring Batman, but Bane underwent the most drastic metamorphosis and became pretty much an opposite of what he was in the comic books. In the movie, Bane was an illiterate, growling bodyguard for Poison Ivy and sometimes repeated the last word of Ivy's sentence.

Paul Dini: We have seen the criminal masterminds who match Batman with combination of physical might and cleverness, and I think [on Batman & Robin] they wanted to go the other way with Bane (Anthology)

Typically for the motion picture stories of Batman, his story/origins were tied up with another character, in this instance it was Poison Ivy, whose experiments with plants helped in creating Venom -  a supersoldier formula constructed by Jason Woodrue (in the comics known as Floronic Man, Atom's villain).

Woodrue uses the experiment on Antonio Diego, a convict who, when injected with Venom directly into his brain, literally inflates like a balloon changing into a loyal supersoldier - that portrayal is more so based on Tim Slaycroft rather than Bane.

Bane was played by Jeep Swenson, a professional wrestler who has passed away since. His entire body was covered in makeup, showing how Venom affects his body and spreads in his veins

Bane's last name, Diego, tells us that just like his comic counterpart he is at least partially Puerto Rican. The Diego incarnation of Bane was played by Michael Reid MacKay

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THE DARK KNIGHT RISES

Christopher Nolan: He's a great sort of movie monster, but with an incredible brain, and that was a side of him that hadn't been tapped before. Because the stories from the comics are very epic and very evocative–very much in the way that Bruce Wayne's origin story is epic and evocative. We were looking to really parallel that with our choice of villain. So he is a worthy adversary. (Empire Mag Jan. 2012)