This summer's superheroic vows of chastity:
Okay, now that you've consented to be spoiled, our two abstinent heroes are the Hulk and Hancock. Actually, in the case of Hancock, it's not strictly true that he can't have sex — according to early screening reports, he simply has to be very, very careful where, and how, he ejaculates. In one scene from Hancock (which had the original title of Tonight, He Comes) Hancock has brought a cute young thing back to his trailer, and they're getting busy. But then Hancock gets close to his climax, and warns the woman to back way, way up. Hancock gets off — and we see his semen riddle his ceiling with holes, almost like bullet holes. (Comics afficionados will not be surprised to learn this scene is ripped off from a Garth Ennis comic.)
As for the Hulk, there's a scene in Friday's new movie where Bruce Banner is in a motel room with Betty. They start to do what the young people do in motel rooms, and Bruce's heart-rate monitor gets more and more bleepy. His heart is pounding with the excitement of making out with a vacant-eyed Liv Tyler, it's too much for him, he's losing his shit, he's going to, oh my god, he's going to... he's going to... Bruce pulls away from Betty just in time to keep from becoming the Hulk. Yes, he can't get sexually aroused without Hulking out. (And I am not going to make any jokes about whether you would like him when he's horny. I'm better that that.)
A digression: Can the Hulk really not get laid?
I'll get to the list of other sexually frustrated heroes in a second. Since I've read almost every Hulk comic ever published (except I admit Bruce Jones lost me after a while) I should stick in a little dissertation about the Hulk's sexual history. Can the comics version of the Hulk really never have sex? We know that the Hulk is Incredibly, perhaps Unfeasibly, well-hung, because the Hulk gets naked in Incredible Hulk #400 and his arch-enemy The Leader remarks on how well-endowed he is. But it's strongly implied, during the "gray Hulk" period, that the gray Hulk — who's working as a Las Vegas leg-breaker — is getting laid on a fairly regular basis.
Bruce and Betty have sex at least twice that I can think of. Once when they first get married, after Bruce has been "cured" of being the Hulk (so there's no danger of Bruce Hulking out.) And once when Bruce gets his pathology backwards, so he's either a peaceful Hulk or a savage, rampaging puny human. In his "savage Banner" form, Betty has sex with him and this calms him down.
There's also the famous sequence in Hulk #300, where the Hulk has gone completely berzerk and Bruce's influence is all gone. The Hulk is trashing New York, and Eros, "the creepiest Avenger" tries to subdue the Hulk using his psychic abilities to generate "waves of pleasure." He learns the hard way that you shouldn't try to pleasure the Hulk in the middle of his rampage. Still more evidence, I guess, that the Hulk and sex don't usually mix. Unless he's gray.
(Update: Commenters have pointed out that the Hulk hooked up with Caiera The Oldstrong in Planet Hulk, the greatest Hulk storyline ever. But she's an alien who's almost impervious to most harm, so it's slightly different.)
I can't have sex, or I'll steal your powers/life/money:
Poor Rogue from the X-men. She's got the cool Susan Sontag hair, and the leather jumpsuit, and the hot boyfriend... but she can never touch anyone. Whenever she does touch another person, she absorbs their memories, strength and physical abilities. She also steals people's superpowers with her touch. She's tragically untouchable. The sexual frustration is so horrendous, it drives her to get rid of her powers in X-Men 3.
I can't have sex because I'm a robot, with non-functioning sex parts:
Beautie is one of the members of the Honor Guard, one of the main superhero teams in Astro City, Kurt Busiek's fictional superhero town. She's always looked like a Barbie doll, but we've never known much about the robot girl — until Busiek published the Astro City Character Special: Beautie last February. There, we see some "pick-up artists" try to hit on Beautie, only to be told that she has no genitalia. None whatsoever.
Other robot or cyborg superheroes who can't have sex include Robotman from the Doom Patrol and Vic Stone aka Cyborg from the Teen Titans. But this isn't true for all robo-heroes, as Star Trek's Data would tell us. The hordes of comic book sex-perverts are pretty certain that the Vision, the android member of the Avengers, did in fact get it on with the Scarlet Witch when the two of them were married.
I can't have sex because my super-strength will end you:
Hancock sort of belongs in this category, since his sperm are deadly to human females. So, too, does Superman, according to Larry Niven, who famously thought way too much about the implications of Krypto-sperm. Besides the speeding-bullet properties of the sperm themselves, there's the fact that Superman might cause an injury if he got too excited during intercourse — and according to the movie Mallrats, the sperm would probably tear Lois Lane's fallopian tubes apart as well. Some self-proclaimed experts also believe Wonder Woman is incapable of having sex with a normal human, for similar reasons.
Spider-Man, meanwhile, has a slightly different problem: He can have sex. But prolonged exposure to his ummm... radioactive bodily fluids eventually kills his wife Mary Jane in a future dystopian story, Spider-Man: Reign by Kaare Andrews.
No sex, please, I'm dead.
There are a surprising number of superheroes who are dead, either undead or ghosts... and most of them never get laid. I'm thinking of Deadman, who's insubstantial except for when he takes control over a living body. (And his ethics might prevent him from using someone else's body as a vehicle for sex, I'm guessing.) And the Spectre, who's basically the spirit of vengeance — he can become tangible, but I'm highly doubtful he ever gets any. (Although the Ostrander run on The Spectre did get a bit saucy at times.)
And then finally there are a number of superheroes whose bodies are just not compatible with anybody else, for various reasons. Like Mogo, who's an entire planet and a member of the Green Lantern Corps. Who can Mogo have sex with? Element Lad from the Legion of Superheroes was celibate for a long time because he was the last of his kind, but did finally find love with a member of the Science Police who took a sex-change drug. There's Negative Man from the Doom Patrol, who's basically a radioactive mummy who has to wear protective bandages at all times, and (I think) can never touch anybody without the bandages in the way.
Update: I totally forgot I was going to write a whole thing about Ben Grimm from the Fantastic Four in here, because it's hinted at various times that he has nothing but more rocks under his little shorts. His girlfriend, Alicia, dumps him and starts dating Johnny Storm, the Human Torch. She makes it pretty clear that this is the first time in ages that she's gotten any action — meaning she wasn't getting any when she was with Ben. Poor Ben.
Thanks to Douglas Wolk for research help!