"Hey, y'all, prepare yourself for the rubber-band man..."
—The Spinners, "Rubberband Man"
A character with a limited Voluntary Shapeshifting power, that results in his body acting like it is made of rubber. This can be a very versatile ability, as long as the user is creative, and not afraid to look silly. Because of this, it tends to be a power of Fun Personified characters.
Such characters often have powers that work less like having a body with high elasticity, and more like being able to change shape at will. Shaping oneself into rubber balls, balloons and bands, flattening against walls, pretending to be a funny-colored rug, gliding like a parasail, folding oneself into a paper airplane, all totally plausible. He is also resistant to physical attacks since he can stretch out his body to absorb the momentum of the object, and then snap it back as a counter attack. What exactly becomes of one's bodily fluids and organs is, of course, never addressed (unless written by Warren Ellis who explains all for Ultimate Mr. Fantastic).
This power is rarely seen on female heroes. Many people joke about the Power Perversion Potential of men with this ability, assuming that they can apply their stretching powers to body parts ordinary people can't consciously move. At any rate, a sufficiently bawdy writer might point out that stretching and reshaping other appendages could still be greatly appreciated by one's partner.
Has nothing to do with the Leatherman, the straw man, or the Slender Man.
As a note, he's more literally rubber than most examples—it requires energy for him to stretch himself, when released he snaps back into shape, and he's highly resistant to electricity and some blunt-force attacks (like maces). He's even learned how to vulcanize himself, via Haki.
Plastic Man, originally of Quality Comics, has the classic jokester personality. Ironically, he started as a serious guy with somewhat silly powers who evolved into a fairly ridiculous character who came up with progressively more bizarre shapes to assume (although even at the end of his first appearance, he commented, "Fighting crime sure is fun!")
Offspring, Plastic Man's son in Kingdom Come, is a completely dour and serious individual who is sick of the "silly stretcher" stereotype and can't stand his father.
In the comics, on the rare occasions where Elongated Man and Plastic Man meet up, a bit of friction between them becomes apparent; Plastic Man's powers are straight up better, pretty much making him a shape shifter, but Elongated Man can simply... become longer, not change shape. On the other hand, Elongated Man is a brilliant detective said to be Batman's equal.
Among the various superheroic personas adopted by Jimmy Olsen during the Silver Age was "Elastic Lad". This eventually led to an issue of DC Comics Presents where the three stretching heroes were teamed up with Superman to fight a one-shot villain who also had stretching powers.
Elastigirl of the Doom Patrol, pre-dating The Incredibles by nearly forty years, was a stretcher (who admittedly rarely changed shapes) who could also grow and shrink. Her size-changing powers were the only ones she used on Teen Titans.
A female stretcher is the villainous Madame Rouge (not Rogue!) of the original Brotherhood of Evil. See also, her 'daughter' Gemini
Although he has been known to goof around with his powers, particularly while playing with his children.
Two What If comics gave Sue this power instead of her invisibility and force fields, making for a rare aversion of the "always male" aspect. What If #6 gave all the four different power sets; What If volume 2 #11 used four short stories to give them all the same powers. In the second one Sue was annoyed at her "silly-looking" power. She married Ben and supposedly they never used their powers again. In the first story, however, she loved her powers and was a much more proactive superheroine than the main Marvel counterpart at the time. This Sue also married Ben, since Reed had mutated into a giant brain which obviously couldn't suit her physical needs.
Warren Ellis, being Warren Ellis, gave him a plausible if slightly Squicky anatomy; no internal organs save a pliable aerobic bacterial stack that isn't torn by his stretching. That's right, tropers. He's a human stress ball with a sourdough starter for a heart.
One of Spider-Girl's villains is a Cloudcuckoolander named "Mr. Abnormal", whose name describes his personality. Ironically, he seems to be more creative with his powers than Mr. Fantastic, shaping his limbs into such things as nets, tennis rackets, ramming horns, and elephant's feet. Being that he was actually a pastiche of Plastic Man, this makes perfect sense.
Super Skrull, being All Your Powers Combined esque for the Fantastic Four of course has this power as well. Once he´s used this and the Thing´s superdurability to make paper thin razor wire of himself. Pretty awesomesauce.
Xavin from Runaways has the same powers as the Super Skrull, but can only use them one at a time.
Angelo Espinosa, a.k.a. Skin from Generation X, possessed approximately six feet of extra skin. He was capable of stretching, deforming, wrapping, expanding, and compressing this extra amount of epidermis like all the other examples on this page, but in much more limited ways; where Mr. Fantastic might be able to reach across or even around a city block, Angelo would strain to reach across a street. In addition, he had very little elasticity, and his bones remained solid and couldn't be reshaped. He could never turn into a bouncing ball; even if he could reshape himself enough for that, he wouldn't bounce.
Wildguard: Casting Call featured two: Longfellow, whose catchy name and snappy costume couldn't make up for his dreadful personality, and Snapback, a friendly, energetic guy with something to prove and an overbearing girlfriend. Snapback's previous superteam experience gave him the definite edge and eventually drove him to make the team itself.
The tendency for this powerset to belong to a goofy character is mentioned by Snapback's bitter Tri-County Power Patrol teammate Sandoval, who tries to dissuade him from entering because "stretchy guys are only ever used for comic relief."
Alan Moore's Top 10 briefly featured "Dr. Incredible", modeled after Mr. Fantastic. Smax calls him a "blob-job", to which he responds, "I don't gotta put up with that shapeist stuff!" Dr. Incredible, however, is an old washed up hero who smacks his wife; not a fun loving guy.
Big Bang Comics' Protoplasman, who, like all Big Bang heroes, is a pastiche of a Silver Age DC character, in this case Plastic Man.
Hack/Slash had a disturbing variant in the form of Monster Clown Mortimer Strick. His skin doesn't stretch, his bones do.
Rubberman, a villain from Air Fighters Comics, could stretch his body and even deflect bullets.
Rubbernecker, from Adam Warren's Empowered has this; despite his name, he can elongate his neck, his limbs, and his torso, and when he swings his mace-encased fists or mace-helemeted head at someone, can do a great deal of damage.
Ping the Elastic Man: A character from the Anthology ComicThe Beano, he first appeared in the comic's first issue back in 1938. His Rubber Man abilities are often Played for Laughs with the character ending up being tied in knots at the end of the strip.
Polly Mer from PS238. Yes, that's her real name. It's implied her father has a really bad sense of humor and her mother is none too fond of it.
Lastikman, a Filipino superhero from Mars Ravelo, the same creator behind Darna.
In CSI Death By Chocolate, Mike Teavee, now an adult, still has side effects from being stretched ten years ago. As such, he is able to do such things as squeeze through a mail slot in a door and stretch the entire length of the precinct room (though hilarity ensues when he loses his grip). Once he is caught, his potential for slipping free of handcuffs is foiled my simply tying his arms in a square knot through the legs of an interrogation table so Brass can question him.
Helen Parr, aka Elastigirl, from The Incredibles. The director, Brad Bird, has said in the DVD commentary that the family's powers are tied to their personality; as a busy mom, Helen Parr is pulled in many directions at once. Throughout the film, Helen is used as a life raft, a parachute, a fire blanket, and a giant set of cargo tiedowns.
In The Specials, rubber superheroes are very common in the Pacific northwest, apparently due to the flouridation of the water there. Unfortunately, said water is also carcinogenic, meaning rubber-men don't tend to live very long.
The titular protagonist of Kamen Rider Double can stretch his right limbs when equipped with the Luna Memory. The Luna Dopant from The Movie is another example, of course.
Parodied/deconstructed in thisMad TV sketch. The military has indeed created a "super soldier" with "rubberized muscles." The end result is that he lacks rigidity and muscle strength to do much of anything, including standing up.
KecoMaster is very well known throughout the deviantArt fandom (not to the extent of the 4 above, but enough that he can technically put himself in the Top 5 with them) for his more cartoony focus on the elastic power potential, and is currently working on a project to draw at least one elastic character from every person he could find who made one on dA!The first two pagesare right here.
Captain Silver from the obscure Capcom Beat 'em UpBattle Circuit. Here, rubber powers are interpreted as a form of shapeshifting, a la Plastic Man.
Sonic Unleashed's Sonic the Werehog has the ability to stretch his arms out at great lengths to make up for his lack of speed.
And years before the Werehog, Chaos was able to do the same stretching with some of its attacks in the early boss fights against it - although, it's technically a sentient creature of water, so it's not quite rubber. Fans think these two things are related due to how similar they are, however.
Ristar can also strech his arms out at great lengths to make up for his lack of a jump not twice his height (as is typical for most platformers). He also uses it to headbutt enemies.
Elastic Man of Brad Guigar's Evil Inc., is a fairly straightforward Plastic Man ripoff down to him being the designated comic relief. Seems to be made entirely out of a green gel and cannot change colors.
Several characters in the Whateley Universe, including Jody Cooms (Plastic Girl) who has the 'Reed Richards' power set. She's more the friendly, helpful type rather than the fun-loving type. She's also cute but not gorgeous and a little overweight, while she lives on a floor with a number of girls who would make Hollywood starlets binge in envy.
Reach, from the same series, is an especially interesting example: he has the Rubber Man power set, but doesn't have some of the Required Secondary Powers that would let him make really effective use of it; namely, while he can make his arm fifteen feet long, doing so stretches his muscles out so much that he can't do anything with his extra-long arm. Near the beginning of the story, however, a lab accident grants Reach the "exemplar" power set, which, among other things, includes Super Strength, so she (oh, yeah, that lab accident also turned him into a girl) is now much more effective.
In the Global Guardians PBEM Universe, several characters have these powers (to the point that "Bendy Toy" has become a commonly used in-universe term for people with such powers). Bungie, a member of the Global Guardians team, is most notable, but other good examples are Embrace (a villainess who combines this with superhuman strength) and Elastorang, a sentient orangutan rubber man.
Static Shock has Adam Evans, The Rubberband Man. He's a little too serious and dour for his powers, but he's apparently beloved by the creators, as he undergoes a Heel Face Turn, dates the hero's older sister, and is revealed to be the brother of the series' biggest Big Bad, Ebon, who himself has similar abilities. His name is a pop-culture reference to the classic Funk tune by The Spinners.
Madam Rouge from Teen Titans is known to be one of the most dangerous criminals in the Teen Titans world, and can stretch her limbs for entire city blocks, and is resistant to physical harm.
Drawn Together had Captain Hero's old college friend-with-benefits "Unusually Flexible Girl", who he liked for the obvious reasons, and who he promised to marry if both were single at age 30.
The Venture Brothers spoof of the Mr. Fantastic is Dr. Impossible, the only one of the Impossibles to have a useful power.
Mr Tickle in The Mr. Men Show can stretch his arms to any length in order to tickle someone.
The premise of the children show Thin Pig, sort of: the eponymous character is bi-dimensional, like a piece of paper, and can fold himself into any tool necessary.
The 2-D Man of the Terrific Trio in the Batman Beyond episode "Heroes". His powers are nearly identical to that of Fantastic Four's Mr. Fantastic. Unfortunately, the entire Trio is Blessed with Suck, as their powers came at the cost of their decaying genetic structure. Eventually, they go psycho and do a Face Heel Turn, forcing Batman to kill them. The 2-D Man is sucked into a high-powered fan and chopped into pieces.
Longarm Prime from Transformers Animated has the ability to stretch his limbs. (Possibly) subverted however, as it turns out it's just a simplified form of Shockwave's shapeshifting ablity.
Kif of Futurama has a mild form of this. Being an amphibian-like alien with no bones, he can stretch himself to a considerable degree, though this causes apparent discomfort and isn't really treated as a superpower.
Ehlers–Danlos syndrome is a kind of connective tissue disorder caused in most cases by a genetic defect in the formation of collagen, which leads to increased elasticity in the skin, joints, muscles and whatnot. Whilst that may sound cool, it goes straight into Blessed with Suck territory. Why? Skin and muscles can become more vulnerable and prone to tearing, joints can be very unstable and dislocate easily and, in the worst-case scenario, the arteries and heart valve can also be affected.