Bomb Disposal

"Some days you just can't get rid of a bomb!"

—Batman, Batman: The Movie

Running into bombs, mines, and other explosives are a pain to deal with, especially if they're blocking your way, hidden, or need to be immediately removed. In fiction, either you can set them off, disarm them before continuing on, throwing them far far away, eating them, etc.

In real life, this isn't so easy. Even with proper equipment, it's a dangerous job disarming explosives. And it's probably worse if you have to set them off using nothing but a stick. Thankfully, there are remote controlled robots that help make the job a little safer.

In shows where physics is on a vacation, expect people to do things like swallowing the bomb or stuffing it into a not even nearly bombproof container, like a paper bag. See also Bombproof Appliance for more "serious" shows.

Related tropes:

Anime and Manga

Senko no Night Raid has a more realistic take on bomb disposal in the third episode: Two are moved using psychic powers to relatively safe places to blow up, while the third is disarmed after Yukina is able to read the memories of the man who built the bomb.
Gunsmith Cats has a few chapters here and there devoted to Minnie May or her boyfriend Ken Taki defusing bombs.
Episode 2 of Rail Wars! shows two of the characters needing to defuse a Time Bomb Hollywood-style, complete with a Magic Countdown and a Wire Dilemma.

Film

The Hurt Locker is so far the most critically acclaimed movie on the subject.
The Mask: The title character disposes of a bomb by swallowing it and letting it explode inside him.
D.E.B.S.: the title characters are trying to defuse a bomb. It activates - and turns out to be a love note from Lucy to Amy.
Lethal Weapon had a nice bombproof bath.
Superman 2: Superman disposes of a hydrogen-bomb set to go off in the Eiffel Tower, by throwing it into outer space... where it just happens to blow the lid of a can of sealed evil.
Hilarity Ensues in Batman: The Movie (1966) when Adam West tries to get rid of a bomb, wherever he's about to throw it, there's an innocent person. Watch it here.
The obscure action film Ticker is mostly about bomb disposal.
The obscure thriller Ten Seconds To Hell is about former German soldiers disarming unexploded bombs in Post World War 2 Germany and actually uses very realistic bomb disposal equipment and tactics.
Heimat features Otto and Pieritz, two engineers, and later, EOD Technicians. Otto dies.
In Batman Forever, Dick Grayson rolls a bomb off the roof of a building and it explodes in the river.

Literature

Starship Titanic has a bomb that really doesn't want to go off.
In Douglas Reeman's World War Two novel The Volunteers, one of the main characters used to be in a bomb disposal unit. He was one of the best at the job, and then one day the latest bomb's Booby Trap activated. He shouted a warning to his assistant and ducked for cover. He survived, but for some reason his assistant didn't go for cover fast enough, and was killed. And the shock of the bomb going off so close produced a bit of short-term memory loss: the survivor doesn't remember whether or not he gave the warning. He's rather bothered by this, naturally....
- Another of Reeman's books is titled Twelve Seconds to Live, this apparently being how long you have if you're trying to defuse a German bomb and the fuse activates instead.
The Frogmen by Robb White is about a frogman in the US Navy. It contains a surprising amount of technical knowledge for a juvenile novel.

Live Action TV

Danger UXB: a 1979 ITV series about an army bomb disposal unit in Britain during World War Two.
There's an episode of Dads Army where Wilson and Mainwaring find themselves in a bank vault holding an unexploded bomb that's dropped out of a German plane. True to the nature of the show, the bomb disposal expert is little help and wacky hijinks ensue.
In the Foyle's War episode "War of Nerves", a bomb disposal crew finds a hoard of cash at a bomb sit and decides to steal it; smuggling it out in the bomb casing.

Tabletop Games

In Warhammer 40,000, the Orks use Gretchin as primitive demining tools: throw one into the suspected minefield, let it walk around until it blows up, and throw another one in, repeat until completely cleared or bored, initiate WAAAAAAAAAAAAGGGHHHHHHHHHHHHH!!!!! charge.
- Not that Orks mind if other Orks get blown up, mind, but it's funnier with gretchin.

Video Games

Minesweeper
The Knights of the Old Republic games had this as a skill. If your skill level wasn't high enough, the mine would go off.
In Metal Gear Solid 2, bombs can be disarmed with a coolant spray that freezes them.
In Half Life 2, Gordon can pick up Combine hopper mines with the Gravity Gun, which doesn't merely disarm them, but resets their target sensors to consider Gordon an ally. This is all due to some questionable design elements that weren't really flaws until the gravgun came along.
- And in Episode 2, you get to destroy one of the minespam choppers by throwing its mines at it.
"Mattel Electronics presents... Bomb Squad".
Counter-Strike: it's the whole point of the "bomb defusal" missions for the counterstrike team after the bomb is set by the terrorists. Normally takes a bit of time, but is faster if one has a "bomb defusal kit".
- Or the Remover tool: link
One driving mission in 'Die Hard Trilogy 2 has you delivering bombs to a disposal facility. One two many bumps makes your truck explode. Later, you have to evacuate a Time Bomb from Hoover Dam before it detonates.
Team Fortress 2: the Demoman's Sticky Bombs can be destroyed using any weapon that shoots bullets, any melee weapon (if one is brave enough), the Scottish Resistance, or Short Circuit (which can also destroy Grenades from the normal Grenade Launcher), or moved away using the Pyro's airblast or any sort of explosion.
The League of Legends champion Ziggs (an explosive themed champ) has a joke the goes "You wanna see how to disarm a bomb?" he then swallows one of his bombs which explodes in his stomach.

Western Animation

In the '90s Spider-Man cartoon, the title character disposes of a time bomb by throwing it straight up right when it's about to explode.
Jonny Quest TOS episode "Terror Island". Race Bannon gets rid of a bomb by throwing it out a window, in the middle of downtown Hong Kong.
- In "Arctic Splashdown," Race threw away another bomb. This one fell practically into the lap of the enemy SCUBA diver who'd planted it.
Futurama, "A Big Ball Of Garbage": When the bomb meant to blow up the ball of garbage is set to blow up too soon, they try throwing it up in the air. The first time they try it, it ricochets off a passing asteroid and back in Bender's hands.
Wallace and Gromit in A Matter of Loaf and Death: a direct spoof of the Batman scene occurs as Gromit tries to get rid of a bomb, eventually settling for throwing it across the Yorkshire border. He fails, and the bomb ends up in Wallace's pants; they have to fill the pants with dough to soften the impact.
Teen Titans: in order to get rid of a powerful explosive in "Titans Together", The Herald teleports it out into space so it can detonate safely away from Earth.
Transformers Animated: to dispose a bomb capable of destroying half of Detroit, the Autobots use a multi-part Fastball Special. Prowl held Bumblebee standing on Bulkheads wrecking ball launcher. Prowl had limited flight capabilities and Bumblebee had rocket jets for that episode, so Bulkhead made the initial launch, Prowl lifted him higher and Bumblebee got even further, throwing the bomb into the lower stratosphere.
Duck Dodgers parodies this with a space mine and running into rooms with priceless works of art, French orphans and simple Amish folk. "Some days you just can't get rid of a Martian space mine."
Stripperella had a parody of the Batman scene above, complete with ducks in the pond. She eventually finds a collapsed tunnel, and uses the bomb to clear away the rubble, freeing the children trapped inside.

Real Life

Subversion: Arch Duke Franz Ferdinand was attacked by a group of anarchists who threw a grenade into his car. He got rid of it by throwing it out. He was later successfully assassinated when his driver got lost on the way back from visiting the people who were hospitalized as a result of the earlier attack. The rest is history.
Draper Kauffman, later commander of the Underwater Demolition Teams, was a bomb tech in London during the blitz. Aside from unexploded ordinance, the Luftwaffe would often drop delayed action bombs with their load to mess with people's heads. While ordinary duds would usually be simple(if dangerous enough) bombs, the later would likely enough have anti-handling devices added to the mix just to make things fun.