Calamity James in The Beano. The entire point of the comic strip is that the universe has it in for him, and the humour comes from the never ending stream of horrible luck he goes through.
More or less every single Big Bad Wolf comic, as well as all Lil Bad Wolf or Three Little Pigs where he plays a part, have him getting the shit beaten out of him by B'rer Bear, Practical Pig, his own son, and pretty much the rest of the universe, no matter whether he's doing something bad or not (granted, he usually is).
Gail Simone has made it a habit of treating Cheshire like this in both her run on Birds of Prey and her Secret Six stories. This seems to coincide with Simone's belief that Cheshire is an evil character, and that her inevitable beat down is Laser-Guided Karma for her despicable actions.
In Bone, the Stupid, Stupid Rat-Creatures are regularly punished for their henching (or one's love of quiche). Their leader, Kingdok, even has Roque Ja make the phrase "Cat got your tongue?" literal.
The title character from Brit. Sure, he's invulnerable, but he gets knocked around constantly. Then it even happens to his infant son whom Brit uses as a club upon realizing that said baby is just as invulnerable as his papa in the last issue (12).
Donna Troy is doomed to suffer in her Post-Crisis incarnation.
The title character from Iznogoud. Iznogoud's scheming makes him a magnet for comic disaster, usually thanks to his schemes backfiring on him. Whatever trap he tries to set for the Caliph - a one-way rocket into space, a portal to an alternate dimension, a potion to turn him into a Baleful Polymorph - he'll end up falling into it himself.
Det. Soap in The Punisher. Some of his highlights include getting dropped on the head as a newborn, finding an ax murderer by getting drunk and sleeping with him, going out with an obvious crossdresser, and accidentally dating his own mother.
In The Transformers: Robots in Disguise; Zetca and Dirge have become this. Zetca (A former Autobot) gets beaten almost to death by two Decepticons after getting into an argument, and then beaten up by another, and almost framed for murder. Dirge (A Decepticon) finds himself bored with the war and makes friends with an Autobot. That Autobot is killed by explosions from the planet (which wasn't his fault), and he's almost killed by the Autobot's superior because he survived. Later, he gets a job at a garbage plant, then witnesses a murder, gets mind controlled, and beaten up. When the autobot Prowl breaks the mind controlnote and subsequently gets mind controlled by "killing" the bot controlling him, he tries to kill Dirge because he witnessed another murder, became one of Cybertron's most wanted because of this incident.
Waspinator shows up occasionally in IDW's Transformers comics, especially the "Dark Cybertron" arc, and isn't much luckier than his Beast Wars incarnation. Within a few panels of his first appearance, he's shot in the back by Bumblebee. Next time he turns up, he's been dragged through a space bridge to hell and back by a titan. Later, Shockwave orders his other minions to kill Waspinator after he's served his purpose, and barely escapes, only to have to go back to serve as a guide for the final assault on Shockwave's lab, at which point he gets impaled by Bludgeon and left on the floor to bemoan his continual misfortune while everyone ignores him.
Many of the characters in Ultimate X-Men have a bad time, but Beast/Henry Mc Coy in particular can't seem to catch a break. Between being disowned, and then used, by his family, tricked into betraying his comrades by an Internet troll, constant angst with his girlfriend, being tortured and experimented on multiple times, and dying — twice — his eventually being killed off for real seems almost merciful.
Razguts/Raznuts in the Warhammer 40,000 comic Deff Skwadron walks the fine line between this and Butt-Monkey. Let's put it this way: only two members of the Skwadron lose a plane Once per Episode. Killboy loses a plane every mission because his flying strategy is based largely on Ramming Always Works. Raz loses a plane every mission because in the event the enemy doesn't shoot him down, his allies shoot him down (and usually make unkind references to turning back to machine-gun him), and when neither of those happen, he crashes.
He also usually ends up bailing out into something nasty, like a Shark Pool or an enemy army. However, he somehow keeps surviving.
Spider-Man: This is what half of the Parker Luck means for Peter. Seriously.