Batman Gambit/Trope Namer

Comics

 * Since the mid-1990s in Comics, Batman's gambits seem to consistently get hijacked by other people -- with disastrous consequences. The JLA arc "Tower of Babel" is an example of this. It's somewhat masterfully combined with a second Batman Gambit specifically designed to keep Batman diverted while his stolen contingencies are being used against the rest of the League:

It's worth noting that, while the League ultimately overcomes Batman's contingencies, they do so only by cooperating and remembering what they know about each other, something they probably wouldn't do under the kinds of circumstances Batman prepared the contingencies for. And the weakness in the hijack? All Batman had to do to stop the entirety of it was to pick up the phone and listen to the rest of the League for more than two seconds.
 * An example of this failing spectacularly comes from Batman as well, in the Wargames arc. Spoiler sets into motion a plan of Batman's which should, theoretically, end up with him in control of all of Gotham's gangs via a proxy. The whole plan hinged on the fact that he was supposed to be present at a meeting between all the heads of the gangs via one of his aliases, Matches Malone. Spoiler went and set off the plan without telling him, and due to his absence, the gang leaders got trigger happy and basically took each other out, leaving a power vacuum that sparked the out of control gang war.
 * In the "Hush" storyline, he finds himself facing off against a mind-controlled Superman, and is clearly physically outmatched. His solution is to have Catwoman dangle Lois Lane off a roof, and give Supes the choice of either saving her or continuing the fight. This trick would never work if he didn't know full well that even a brainwashed Clark would never let Lois die, and that Catwoman is just amoral enough to threaten an innocent woman without actually meaning it. He may even have predicted that Lois' struggles would cause her to fall, adding an element of urgency to the situation.

Batman even managed to set this up without hinting overtly at Superman's secret identity. He simply tells Catwoman that Supes cares about the people who work at the Daily Planet. There are three people there at the time, giving her three options; Lois, Perry White, or Jimmy Olson, any of whom Clark would gladly lay down his life for. It's Catwoman herself that decided Lois would be the best target, so she had no idea she was dangling Superman's wife from a ledge.
 * Darkseid had one for when Batman attacked him: he predicted that Batman would succeed in finding his way back to his own time, so he set things up such that when it occurred, Batman would bring with him a weapon capable of killing the entire JLA. Of course, Batman eventually countered with a Xanatos Gambit of his own, hence the fail condition.

Fanfic

 * In Marvel/DC: After Hours, Batman shows once again why this trope is named after him. Despite naturally not knowing about the events of  he is able to piece together enough clues to know how to.

Films - Animated

 * Batman Under the Red Hood indicates that he taught this to his sidekicks as well. Red Hood hatches a plan that's entirely dependent on the assumption that, when pressed hard enough, Black Mask would Which is, of course, exactly what happens.

Films - Live Action

 * Ironically, every single thing the Joker does in The Dark Knight Saga is a Batman Gambit. This is perhaps the most obvious when he is If, at any point along the line, the police had acted differently than he'd anticipated, none of this would have worked.

It should be noted that this was apparently the Joker's Plan C. The cops were obligated to give him a phone call when they arrested him. When they didn't, he demanded one before revealing where the hostages were. When he ran out of time on that, he manipulated the cop. If that hadn't worked, he presumably would have had a plan D up his sleeve. This example is a bit egregious since the Joker's Batman Gambit relied on an urban legend (the police aren't necessarily obliged to give you the fabled One Phone Call.)
 * Well, he did have a blade to the cop's throat at the time. It was less a case of getting a call he was legally entitled to and more a case of obtaining demands with a hostage.
 * And there's good reason to suspect he did in fact plan for it all to happen then. Joker couldn't have escaped until Batman had gone after the hostages, so asking for his phone call was probably just a setup for later when he demands it.

Western Animation

 * Batman: The Animated Series:
 * The episode "The Cape and Cowl Conspiracy" (based on an earlier comic story) had a crime boss hire a specific villain with a penchant for death traps to hunt down and get Batman's cape and cowl. After several attempts, he managed to do so, apparently outwitting the great Batman. Upon returning the items to his employer, the crime boss asked about a recent job the villain did concerning miscellaneous important items. After he explained the job, the crime boss revealed himself to be Batman, who organized the entire ordeal so that the villain would reveal where the items were as well as have the key to the locker holding them. If Batman had thwarted the death traps and captured him conventionally, they probably wouldn't have gotten any information or the key from him.
 * Harley actually manages to outsmart Batman -- more than the Joker ever could -- so he whips out a Batman Gambit and convinces her the Joker wouldn't believe she could pull it off. So of course to prove it she brings the Joker to Batman... right where he wants him, because Joker would never let anyone else kill Bats, making this a Batman Gambit that used Harley to pull a Batman Gambit on the Joker. All while chained upside-down and half-conscious.

Of course, this all started because Harley nailed a Batman Gambit on Batman. She pretended to be betraying Joker by giving his plans to his worst enemy, on the condition that Batman protect her from her boyfriend's wrath. Then she rigged a robotic Joker decoy to attack her and Batman at the rendezvous point. Batman did as he had promised - he tackled Harley to shield her from the bullets. If he had not done so, she would never have been able to get close enough to him that she could stick him in the back with a needle full of sedative. No wonder he was impressed.
 * Justice League:
 * Batman pulls a particularly brilliant one, outwitting what essentially amounts to the Injustice League and getting them to undermine their own plans and betray one another... all while immobilized in a full-body restraint system in the basement. He proceeds to tell that he could've escaped at any point he wanted, but only stayed around to keep an eye on him.
 * In "Wild Cards," when he talks to Harley Quinn suggesting that the Joker's likely more interested in the girl he's standing next to on TV while he sends Harley out to do the grunt work. She refuses to turn on the Joker and seemingly knocks out Batman then returns to the Joker to talk things out. Joker promptly slaps her aside, quickly realizing that it was all Batman's plan to get her to return to base and lead him to his headquarters, which is just what happened.
 * There's also a double Batman Gambit -- both carried out by Bat...men! Justice Lord Batman tries to convince our Batman to join the cause, but Bats ends up reversing it.
 * During the same episode, The Flash is imprisoned with the rest of the good Justice League, and Justice Lord Batman is told to guard them. In the middle of his shift, Flash seems to go into cardiac arrest. Justice Lord Batman panics and rushes to revive him, only to find that the Flash is still very much alive after he knocks him out with one hand. Flash knew that something bad happened to the alternate Flash, and that Batman would not want to watch that happen again. If the bad Batman had not had the same emotional difficulties with losing people he loves that the good Batman has, the plan wouldn't have worked.

And then, when Flash releases the good Batman, he reveals yet another such gambit. He knew that the Justice Lord Batman would watch him more closely than the others, and probably catch on to any escape plan he had. However, the bad Batman wouldn't expect such a thing coming from Flash, and so Batman's gambit was - just to wait and see what the kid came up with. It worked for both of them.