Easily-Detachable Robot Parts

Some robots are apparently constructed of easily detached (and easily reconnected) parts. An arm fell off? The head fell off? No sweat, just screw or push it back on, since they usually are as easy to connect as LEGO. Use it as a weapon, why don't you? Sometimes it appears that each of their parts is self-sufficient and can function on its own.

This is generally justified by having the power source and CPU being the only real parts that matter; everything else can be repaired or replaced. Kinda makes sense when you look at a computer, which will continue running as usual after you unplug everything but the power cord. That doesn't stop it from not making sense at times.

Can get a bit ridiculous if the robot is easily rebuilt after things like explosions, which logically should mishape the parts that reconnect. To go to the computer analogy, your PC will work if you take anything but the power cord out, but it won't work that well if do something like shoot it with a shotgun. (On the other hand, sometimes things do work after bending.)

Examples of Easily-Detachable Robot Parts include:

Anime and Manga

The eponymous robot of Dai-Guard tends to lose an arm in every fight. This is weaponized by Akagi in the third episode, and later elevated to an actual function of the machine, with its advanced weaponry replacing one or both of its arms.
A lot of Mobile Suit Gundam series loves to do this, especially if the mechs use a Core Block System:
- In Mobile Suit Gundam 0083 Stardust Memory, Kou Uraki separates the GP-01 Fb's lower torso from its upper torso to escape the Val Varo and land a killing blow.
- In Mobile Suit Victory Gundam, the titular mech can actually launch its components, the Top Fighter (its arms and chest) and Bottom Fighter (lower torso and legs) at opponents. Justified as the League Militaire have TONS of those things.
- In Mobile Suit Gundam SEED Destiny, Shinn Asuka uses this expertly in his fight with Kira Yamato between the Impulse and the Freedom, including the same separating at the waist maneuver Kou pulled off and even launching the top half of the Force Impulse at the Freedom and making it explode!

Comics

In the short-lived 1980's Archie Comics series Man Tech, both the cyborg good guys and the robot bad guys had modular parts. The comic was based on a toy line that had this characteristic.

Film

C3PO, of course.
- One of the Expanded Universe guidebooks indicates that most protocol and translation droids are made this way so that they can take abuse from owners who like to Shoot the Messenger.
The T-1000 is a borderline example, but it *was* a robot. Albeit a liquid metal one, with detached parts reverting and being reabsorbed into the main mass.
The Iron Giant is so modular that individual screws are intelligent enough to track down the rest of the body if misplaced.
WALL-E. Apparently he's specifically designed so he can replace any of his damaged parts himself, with absolutely everything being modular.
- Justified; he is an industrial robot designed to take care of himself for long periods of time, and the only one that activated properly, so he's got plenty of spare parts...
- Alternatively, the WALL-E industrial models lasted a while, but our protagonist was the only robot of his model that lasted this long, due to being a notch smarter and more curious than the rest, and figuring out how to repair himself using the corpses of his brethren.
- EVE's head and arms are even more easily detachable, since they just float alongside her body, as if they're connected by some kind of energy field. This creates some confusion for WALL-E in the repair ward.
Johnny 5 from Short Circuit (and, presumably, every other SAINT robots) are built like this; each Nova truck is full of parts for them, and Johnny uses them to at different times replace an arm that went dead (which, apparently, was being held on at the shoulder joint by just magnets) and building an entire duplicate to get blown up by the military for him.
In the Hitch Hikers Guide to The Galaxy film, Arthur detaches Marvin's for use as an improvised weapon, despite having no tools handy (unless Ford's towel is that cleverly made).
The short film I'm Here is centered around a male robot selflessly giving his love interest his limbs as she accidentally damages hers beyond repair. He can detach them in a matter of seconds with a screw driver stored in his finger tip.

Literature

The existence of a robot designed like this was a major plot point in The Naked Sun, a science fiction murder mystery by Isaac Asimov.
Vuffi Raa from the Star Wars Expanded Universe can detach his five tentacles from his "body" and have them do tasks by themselves. The tentacles even have enough individual intelligence to operate starship guns, thus allowing Vuffi Raa to get around his Thou Shalt Not Kill programming.

Live Action TV

A Public Service Announcement features Astar, a robot from the Planet Danger. He can put his arms back on. You can't, so play safe.
Data (and by extension Lore) on Star Trek: The Next Generation. Although Data is shown to be extremely strong and durable under most circumstances we are shown in one episode that his limbs can detach with a simple twist.
Kryten from Red Dwarf.
In the Doctor Who episode "The Pandorica Opens", Amy and the Doctor encounter a Cyberman who has his head and arm removed and all three parts are capable of acting independently.

Video Games

Alisa Bosconovitch of Tekken 6 is a Robot Girl with a detachable head. An exploding detachable head. She even has alternate intro and victory poses where she's either carrying her head or it falls off while she's talking.
The combot parts of all factions (murderous precursors included) in Metal Fatigue are perfectly compatible with each other. Lopped off the axe-toting arm of your opponent with a katana? Eject your useless energy shield arm out of its socket and graft his weapon on in mid-melee. Humiliation ensues.
Cyborg Justice was a great example of this; among your various hand-to-hand combat moves, you could yank off your opponents' arms and replace your own with theirs; you could also yank their torso off their legs, absorb their life force, and then steal their legs too. Nothing says pwnage like stealing all your parts.
In the "Day of Sigma" movie in Mega Man X: Maverick Hunter X, X at one point simply drops his buster off, then it turns back into his forearm by itself.
- Both Junk Man and Mino Magnus are good examples. Junk Man, as his name suggests, was a robot made out of spare parts and assorted trash held together by electromagnetic forces. Said forces can be easily disrupted by Cloud Man weapon's Thunder Bolt causing the trash titan to fall appart. Mino Magnus was the boss of the Magnetic Zone and could generate huge amounts of electromagnetic power. In battle, Magnus used said power to separates his body into five parts, attacking Zero with a rather complex pattern of movements.
In the Angband Steampunk variant Steamband, the player races Automata and Steam-Mecha use robot parts in lieu of some clothing items, and mostly advance by finding or buying better versions of these. Thus, various types of heads, torsos, arms, and legs are entirely swappable. (This also means that the lack of all of these won't prevent a character from certain basic functioning...) Given the extreme speed at which certain monster automata can reproduce, they may be designed along similar lines.
In Space Quest 6: The Spinal Frontier, Roger asks Circuit Sydney, the resident android on the DeepShip 86, to lend him his eye and an arm. Sydney is a little reluctant at first, but Roger promises to return them. They come off easily.
Though not exactly a 'robot': in Pikmin, Olimar's ship is scattered into intact parts when it crashes. All that's needed to restore the the ship is to recollect the pieces. (Though, to be fair, Olimar does mention making a few repairs)
In the My Sims, Makoto, despite being a typical high school girl, loses her arms from time to time, including, in My Sims Agents, during her "Prom Date" mission if you have her do "The Robot" instead of the waltz for the final dance.
The page image is from The Legend of Zelda: Skyward Sword, of the boss Koloktos: throughout the battle, you use a whip to pull its arms apart, and then you swing at the Heart Drive with one of its dropped swords. While, after a brief amount of time, it is able to use some sort of energy to reattach its arms, it is unable to repair the damage on the cage it uses to protect the Heart Drive.

Web Comics

Helix from Freefall. All his limbs - head included - are easily detachable and modular so if he loses a piece, you can just stick it right back in the slot - since he's an industrial robot designed for carrying heavy objects, it makes sense - being able to easily shed a limb ensures that he won't easily be pinned under a fallen object, and user-friendly reattachment makes repairs a breeze. (The reassembly is idiot-proof, though definitely not Sam-proof.) Unsurprisingly, he gets taken apart a lot, but he doesn't really mind - it's usually Florence who puts him back together again (though she's usually also the one who took him apart in the first place), and being the brilliant engineer that she is, she usually puts him back together BETTER than he was...
Pintsize from Questionable Content is held together in much the same manner as Helix, with contained-field magnetics that allow him to be put together however you want. And also pulled apart without incurring permanent damage.
The robots from Gunnerkrigg Court seem to be this, as Antimony (who, by her own admission, doesn't know the first thing about robotics) was able to reconstruct Robot S13 from a box of parts (i.e. torso, arms, legs, etc.). On the other hand, actual damage to these parts is not so easy to repair.
In The Inexplicable Adventures of Bob, after Fructose Riboflavin deactivates his robot guard to escape from prison, he removes the guard's Arm Cannon to use as a gun. It's too big for him to cart around, so he sets it on a wheeled tripod.

Western Animation

Bender from Futurama.
- Taken to absurd levels and lampshaded as early as the first episode: A scene opens with Bender using one arm to put his other arm on, with the view so close that we can only see the act itself. Then the arm that was just screwed in picks up the first arm, and the camera pans to the second arm attaching the first to his other shoulder. Fry then remarks that he has no idea how that was possible.
Played for laughs in a torture scene in The Venture Bros The Monarch's henchmen try to rough Helper up but knock off his head, making them realize there isn't much they can do to the robot.
Cyborg of Teen Titans.
XJ9 from My Life as a Teenage Robot, although she does require a lynchpin to hold her body together. May not count; instances of losing and reattaching limbs are rare. But then, armed with a wrench, somebody can turn her into a motorbike.
Larry 3000 from Time Squad.
The Transformers lose body parts all the time and they are simply reattachable. It caused problems in Beast Wars especially, where so many characters get utterly smashed, dismembered, and mangulated for comedy purposes that when someone is Killed Off for Real, the reaction is less "Oh, no!" and more "wait a sec, didn't Airazor turn Terrorsaur into robo-confetti, only for the him to be back to normal by the end of the episode? Dinobot didn't suffer half the damage Waspinator does every week!"
- Hell - in one episode, Inferno was vaporised, only to return in the next one with minimal damage.
- The Junkions are the epitome of this.
- The live-action movieverse seems to be the only incarnation of TF where having your head removed is more than an inconvenience.
  - Though Bumblebee's legs were reattached before the end credits of the first movie, so...