Hector's Clique: The Contested Corpses
This unlucky group is full of people whose bodies caused some conflict after they died. Hector unwillingly joined the club when Achilles killed him, dragged his body around Troy, and left his corpse out in the open for dogs to eat. Luckily for Hector, the gods themselves intervened and his body was eventually given a proper burial. (Big deal alert: otherwise he would've had to wander the world forever as a ghost.)
Ajax
When Odysseus was awarded the armor of Achilles, Ajax went so nuts that he killed a bunch of sheep thinking that they were Agamemnon, Menelaus, Odysseus, et al. After, he was so ashamed that he killed himself with the sword Hector had given him after their duel. Because Ajax had threatened his fellow Greeks, Agamemnon declared that it would be death for anyone to give his body a proper burial. But his brother Teucer was determined to do it anyway, and thanks to some slick talkin' by Odysseus, Ajax's body was eventually buried properly.
Polynices
This son of the cursed Oedipus died when fighting his brother Eteocles for the throne of Thebes. Eteocles died in this civil war as well, and afterward Creon took the throne. The new king declared that Eteocles should be buried properly, but that Polynices should be left to the dogs. His sister, Antigone, wasn't going to have this, though, and caused a whole chain of tragic events by trying to bury Polynices' body. You'll find the whole story in Antigone by Sophocles.
Sisyphus
This tricky guy actually asked his wife to desecrate his corpse on purpose. What the Hades is wrong with him, you ask? Well, Sisyphus was a seriously evil dude who Zeus had chained in Tartarus by Thanatos (a.k.a. Death). Sneaky Sisyphus tricked Thanatos, though, and left the death god chained in Tartarus instead. Knowing that Death would come for him again, Sisyphus then asked his wife to leave his body unburied in the courtyard. When he died, he begged Persephone, Queen of the Underworld, to let him go back up and "punish" his wife for not burying him properly. Eventually, Sisyphus' tricks ran out, and he was doomed to roll a giant boulder up a hill in the Underworld for all eternity.