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.
The hero Jason decided to dump his wife Medea and marry the daughter of the king of Corinth, an act that made him an enemy of his own protector Hera, Goddess of Marriage. But before Hera could make him pay, Medea herself got revenge on him: she burned alive the king's daughter, and, by accident, the king and his palace (the king had tried to save his daughter, but failed and spread the fire), demolished Corinth, in some versions even killed two of their own children (in others it was the Corinthians, who wanted revenge for them delivering the clothes that set the king's daughter on fire. Demolition of the city follows soon after), and leaves with the others. And Jason? Still alive, with his spirit and reputation destroyed and transformed in a beggar. You do not piss off your Magical Girlfriend, for even the goddess known for being ludicrously vengeful won't have the heart to add something on top of what already happened to you...