Pissing off Heracles was unfortunately very easy to do, and never a good idea. Among his many other deeds, Heracles is known for exacting horrific revenges on a number of Greek kings who crossed him. Whether it was King Augeas refusing to pay the cattle he owed Heracles for his cleaning out Augeas's stables, King Neleus refusing to purify Heracles after he killed a man in anger, or King Laomedon trying to get out of paying Heracles the magical horses he owed Heracles for killing the monster that threatened his kingdom, all three of them were eventually invaded by Heracles and his army and slaughtered for crossing him.
In The Iliad, Achilles gets into a spat with Agamemnon and decides that he won't be in a fighting mood for the foreseeable future. When his best buddy Patroclus gets himself killed trying to take Achilles' place, however, Achilles flips right the hell out and nearly chokes the Trojan river with their dead. Even Hector, the killer of Patroclus and first among the Trojans, makes a run for it until he realizes that Achilles won't stop chasing him and decides to go out swinging.
In The Odyssey Odysseus and his son kill all forty suitors who have dishonored their house. In the middle of the slaughter, some of the suitors try to repent and beg for mercy, but Odysseus affirms that he must kill all of them. The gods themselves demand that he take vengeance. Only two survive the slaughter: a bard and a herald. In Homer's time, poets and heralds were sacred, and not to be slaughtered wantonly. It helps in this case that these two really were innocent; the bard had been dragged along by the suitors, and the herald was actually Penelope's spy.