Pull the IV

"You know those cords that connect to your arm whenever you're in the hospital? They're apparently called IV cords and it's a drippy thingy that keeps you alive. I've actually noticed this more than once, but whenever a person (usually an Action Hero) finds him/herself in a medical room and hospitalized, the very first thing that they do to "escape" the room is to pull the IV cord. It's directly connected to your arm's vein, but it apparently doesn't hurt at all; and it could also kill you if you do that."

—Ckretaznman

"Why is it that whenever someone wakes up in a hospital, the first thing they do is pull the IV out of their arm? Maybe it was keeping them alive!"

—Unskippable

IV (intravenous) therapy is a form of medication administration in which the desired medication is given directly into the bloodstream through a vein. Intravenous systems, which consist of a small, thin plastic catheter attached to a needle-less "lock" device, are commonly used by medical personnel to draw blood samples, give one-time "pushes" of medications, or infuse medications or fluids over extended periods of time. (These last are commonly known as "IV drips," as the apparatus consists of a large bag or bottle of fluid connected to a length of plastic tubing containing a drip chamber). According to The Other Wiki, intravenous therapy may be used to correct electrolyte imbalances, to deliver medications, for blood transfusion, for rapid fluid replacement to correct dehydration or blood loss, or for maintenance fluids in a patient who cannot eat or drink.

Healthcare professionals take great care in starting and removing IVs, as the IV site represents a wound in a blood vessel that can bleed significantly or become infected if not properly cared for. However, your typical Action Hero or Badass would much rather dramatically rip the catheter out of his arm and then run off to continue his feats of Bad Assery. It's a simple way for a writer to show the audience that the character has better things to do than sit around getting healed up. This is a trope dedicated to those Bad Asses that can risk wounding themselves without getting into any dire straits.

Not to mention the fact that, for no particular reason, the IV is often shown facing the wrong way even when it is in.

May be related to Afraid of Needles, and represents an amusing subversion: there is no needle in an established IV, as it's only used to introduce the catheter into the vein, and is removed and safely disposed of immediately thereafter.

Examples of Pull the IV include:

Anime and Manga

Yu-Gi-Oh!. Bakura, a character who has a spirit possessing him on and off, is stabbed and passes out. He wakes up in a hospital as the spirit, who promptly knocks out the old man who was watching over him, stands up, violently rips the IV out of his arm, and sets off to find the guy he's planning to defeat. Of course, this is far from the only time the spirit did something detrimental to the health of his host; the aforementioned stab wound was self-inflicted,
When Lady Une comes out of a coma in Gundam Wing, she pulls out her IV and goes to rescue Treize.

Comic Books

Iron Man: Tony Stark not only pulls out an IV, but also his own respirator tubes.
Desolation Jones: Jones was panicking when he pulled out his IV, but a year's worth of trauma kind of justifies it.
The Walking Dead: Zombie apocalypse so justified, but when Rick Grimes does it the wound noticeably continues to bleed throughout the first issue.

Film

In Resident Evil Apocalypse, Alice wakes up alone in a hospital Late To The Zombie Apocalypse, and the first thing she does is yank out the IV. Albeit she does seem to feel pain.
Pretty sure this shows up in the Halloween 2 (remake). Of course there it's a nightmare sequence.
The Bride does this in Kill Bill during the hospital sequence after killing Buck's latest "customer," who he'd been pimping out her comatose body to, just before getting into position (with no working legs, mind you) to ambush and take revenge upon Buck.
Played for Laughs, naturally, in Airplane!. There's a young girl being transported to a hospital, whose IV line keeps getting knocked out by the stewardess playing the (borrowed) nun's guitar.
In The Matrix, Neo has a similar setup, but fed directly into a port in his arm (and facing the wrong way). Removing it does seem to cause pain though.
Inception: The dream machine appears to involve an IV-like device, which appears to be simply pulled out when not needed.
- Raises Fridge Logic issues as to how the dream machine could feasibly be used on someone without their ever realizing it, if their arm is bandaged and sore when they wake up.
  - Saito is shown checking his arm after waking up from the extraction. There's no mark and he feels no pain. The fact that Cobb and his crew were able to do this without leaving a trace clearly impresses him. How they do it isn't explained, but it's clear they've developed a way to do it painlessly and without marking the target.
  - Looking at the schematics of the device itself, one will notice the 'needle' is more like a pair of very small fangs, presumably small enough to go between the cells.
Jim of 28 Days Later does this, though not right away. It's not like anyone's coming to tend to him, and we see him wrapping a bandage around his arm where the IV had been.
Harry Brown of the eponymous film removes his monitors and goes home after waking in hospital following an emphysema attack.
In the first X-Men 1 movie, Wolverine wakes up at the medical room of the X-Men base and promptly rips out the needles. Doesn't bleed thanks to his hyper regeneration.
James Bond does this when escaping from the MI6 medical facility in Die Another Day.
Bob Lee Swagger does this to himself in Shooter; he's been shot and knows he's going into shock from blood loss, so he improvises an IV set using aquarium tubing, plastic soda bottles, and a basting needle. Once he's bolused himself with a liter or so of homemade sugar-salt solution, he yanks the line out and continues on his merry Badass way.

Live-Action TV

Averted in an episode of Moonlighting, where a hospitalized gangster gets into a fight and drags his IV drip around with him. Played for Laughs, obviously.
Faith in Buffy the Vampire Slayer, although in her case it might not just be a matter of Bad Assery but also of not particularly caring what happens to her.
A variation on the theme happened in an episode of House, with a serial killer who yanked out his breathing tube.
Naturally, any TV series featuring an emergency department will show this at least once; notable examples include Grey's Anatomy and ER.
The breathing tube variant also appears in an episode of Royal Pains. Jill asks Divya to have them take her breathing tube out; Divya explains she can't, and so Jill gives her a distraction so she can remove it herself.
In the 2004 remake of Battlestar Galactica, Starbuck does this when breaking out of the Cylon farm.
In an episode of Psych, Henry Spencer, not wanting his son to embarrass him by this whole "barely poisoned" foolishness (thus resulting in his son languishing in a hospital rather than solving the case) yanks the IV out of Shawn's arm. Notably, it has quite painful results.

Theater

In Angels in America, when Roy Cohn is in the hospital for treatment regarding his suffering from HIV, he accidentally knocks out his IV while flailing in anger at a visitor. This does cause him pain as well as cause blood to come out, which the nurse hurries to clean up and warns the visitor to wash off of himself ASAP.

Video Games

Alpha Protocol had this early on, noted in this episode of Unskippable (occurs 2:44, called out at 6:18)

Real Life

People can and frequently do attempt and succeed in pulling out their own IVs, as well as more invasive medical devices (Foley catheters, central venous lines, arterial lines, endotracheal tubes, etc). In the case of a basic peripheral IV, frequently this results in some pain and a big mess, as the drip (if any) will keep dripping all over the place, and the site will continue to bleed to varying degrees if it isn't well bandaged. (How much blood may be involved depends on whether the patient has been given any anticoagulant or "blood thinning" medications, as well as the size of the IV "line." For example, a 14-gauge widebore will bleed much more than a 22-gauge pediatric line.) In the vast majority of cases, a pulled IV is no cause for alarm; it just means the staff will have to stick you again to start a new line. The major risk that may be involved arises from abruptly discontinuing any dripped medication the patient may be on, and the time delay before resuming it.
As most modern indwelling peripheral IVs consist of only a small plastic tube (catheter) sticking into the vein (the actual needle is used only for insertion, the catheter is threaded over it, and then the needle is removed and discarded), there is little risk for further tissue damage from pulling out an IV. Also, IVs inserted the wrong way (as mentioned on this trope page), though definitely not the standard of practice, are sometimes used in real life and can still function.