Elevator Escape

Elevators. We all know and love them. Those wonderful devices that let you reach the thirty-second floor without climbing ungodly amounts of stairs. Those wonderful moving rooms with lots of shiny buttons... including the "Close Door" button. Is Bob running from The Mafia? No problem! He just has to duck into a nearby elevator and hit that button, and the doors will miraculously slide closed just as the goons come running up to them, protecting Bob from their wrath!

Does not actually require the button being pushed to be the "Close Door" button, although it's common for a panicking character to push it repeatedly with a sense of urgency.

A common subversion is for the "Close Door" button to not work. Whether it's deliberately disabled, never connected in the first place, worn out from over-use, or simply doesn't respond fast enough to be noticeable, the fact remains that pushing the "Close Door" button does absolutely nothing. Another common subversion is for the pursuer to stick something in between the closing doors, activating the proximity-sensors and making the doors pop back open.

A bit of Fridge Logic applies when you realize that elevator doors are not bulletproof, so a sufficiently armed member of The Mafia could probably shoot Bob even if the doors did close. Until, of course, the elevator starts actually moving out of the way (see also Concealment Equals Cover). Also, if your enemies happen to have grenades handy (not very common with most mafias but quite common with certain cartels), one of them thrown into an elevator as the doors close or dropped into it from above can ruin your whole day.

Films -- Live Action

Olsen-Banden over alle bjerge (The Olsen Gang over the Hills): Egon is fleeing from the big bad's hired bodyguards into an elevator which seemingly is going down. The bodyguards promptly run down the stairs to chase him. However it turns out that Egon was just going down onto his knee, getting under the window in the elevator door.
Tatopoulos escapes the baby godzillas by elevator in the 1998 american Godzilla film, and has to boot one of the lizards in the head to get the doors to close.
Larry does this in the first Night at the Museum movie when running from the Huns.
Kevin from Home Alone 2 ducks into the Hotel elevator just as the staff is finally getting off the floor to try and grab him.
North by Northwest - Roger needs to flee a hotel before the villain's goons come for him, and he reaches the elevator going down - just as they get out of the next elevator, and promptly follow him in. Roger has his mother in tow, who refuses to believe he's in any danger.
In Terminator 2: Judgement Day, Sarah, John and the T-800 use an elevator to get a lead on the pursuing T-1000 during Sarah's rescue from the mental hospital. It's initally subverted when the T-1000 reaches the doors just as they close and pulls them open, but then immediately put back on track when a well-placed shotgun blast stuns him and the doors close normally.

Literature

Played with in The Dresden Files. Harry is running from three of the Billy Goats Gruff (a lot more dangerous than they sound), and ducks into an abandoned building to escape them. Knowing that they'll soon find a way in, even if they have to bash down a wall, he runs to the elevator and starts pushing the button for the top floor. Being that elevators run on electricity, and Harry is a Walking Techbane, it takes a few tries and lots of near-panic before it works.
Played with three times in Matthew Reilly's Contest. Double Subverted when the contest starts when an alien (Reese) almost breaks through the doors after they closed, but they still escape after shutting the doors again. Subverted properly, when the next alien they try to escape from (Karanadon) this way pulls them back up by the cables. Invoked and Subverted by the Big Bad Bellos so he could trap them by going through the ceiling hatch.
- The personal elevator was used exactly once by the marines in Area 7. Played dead straight, of course they immediately escape through the ceiling hatch anyway because the elevator is a death trap.

Live Action TV

In the Doctor Who episode "Rose", the Doctor and Rose get into an elevator to escape the monsters. One monster is slightly faster than is usual for this trope, and gets its arm between the doors as they close.
- In the episode "World War Three", the Doctor escapes being shot by an impromptu firing squad by virtue of a conveniently located lift.

The Doctor: Ah, well, now, you see, the thing is, if I was you, if I was gonna execute someone by backing them against the wall, between you and me, a little word of advice, (there is a ping and a door slides open behind the Doctor) don't stand him against the lift! (steps into the lift and the door closes)

Video Games

After you confront Dr. Breen in his office near the end of Half-Life 2, he escapes in his personal lift before Gordon can catch him. You have to chase him down to the main reactor before you can confront him properly.
Both Left 4 Dead and Left 4 Dead 2 have campaigns where this can happen, with the survivors fighting off waves of zombies while they wait for the elevator doors to open up. Often viciously averted in VS Mode, when smart infected players spit acid into the elevator or pull a survivor back OUT just as the doors are closing.
A staple way to gain a mid-chase break in Mirror's Edge. Here the doors clearly are bulletproof since their closing is met with a barrage of dents appearing as the trigger-happy Blues spray the area. At one point Faith gets to experience the other side, as Jacknife ducks into an elevator and gives an insufferably smug wave as he disappears.
Midway through Silent Hill 2, James and Maria have to pull one of these off to escape Pyramid Head. Only Henry makes it.

Western Animation

Totally Spies!!: Sam, Alex, and Clover chase a thief into an elevator. The thief, however, escapes through a ceiling panel, cutting the cable. The elevator of course falls down, but stops a couple of times on the way, providing time enough for a Clip Show.