Peloponnesian
One of the most devastating wars in Greek history is the Peloponnesian war. It lasted between 499 and 449 B.C.E
When the Persains retreated, Athens grew more powerful, and three decades of the war followed. Sparta finally won, but was very weakened by the war. After that, Alexander The Great decided to conquer Greece. Since the two major cities had practically destroyed themselves, he marched in virtually unopposed.

Trojan
The Trojan was one of the earliest human wars in Ancient Greece. It consisted of the Mycenaeans and Troy.
Supposedly, the war began after the abduction of Queen Helen of Sparta by a Trojan prince. Helen's husband had convinced Agamemnon, who was the King of Mycenae, to go kick some Trojan butt.
The Mycenaeans were accompanied by heroes Achillies, Odysseus, Nestor and Ajax. They had more than one thousand ships, too.
The siege lasted over 10 years, and finally ended when one night, the Greeks left their camp, leaving a large wooden horse behind.
The Trojans decided to bring the strange 'gift' inside the gates of Troy. When night fell, a large group of Greeks jumped out of the horse and caused havoc inside Troy. Eventually, they got the Spartan Queen back.

The First War
The First War (not the first world war) lasted, by most accounts, 10 years. The war took so long because the people on both sides were immortal. You literally couldn't kill anybody. You had to take each person prisoner, then hurt him/her so badly that he/she never heals.
Easier said than done.
It started because Kronos, lord of the titans, had a prophecy where his kids would destroy him. Five times his wife gave birth. Five times Kronos ate the kids. King Cannibal, right there.
Rhea, Kronos's wife, finally gave birth to her 6th child, Zues.
Zues, when he was old enough, went to Kronos's castle, applying for a job as cup bearer. When Kronos wanted a drink, Zues went to get it.
After a while gaining Kronos's trust, Zues decided to get his brothers and sisters back. Some stories say he mixed mustard and wine into a drink for Kronos. Others say he mixed herbs. Since Dionysus hadn't come around yet, I'm assuming Zues mixed the herbs.
When Zues got Kronos to barf up his brothers and sisters, they were so grateful they decided to let Zues lead them. Zues started a war with the Titans, but only the male titans would help Kronos. The females were too scared.
In fact, two male titans even joined Zues!
After ten years, Zues finally got the upper hand and became King of the universe. Kronos was, like the prophecy foretold, destroyed by Zues, and thrown into Tartarus, the pit of darkness in the underworld.
Such a happy ending! :)