The Greeks were the first civ I played as in a skirmish game when I got AoE I so they are special to me.
In my case, I love the Egyptians. They are probably the most cliché civilization out there, though
They are the first to appear while opening the Scenario Editor, by the way.
Assyrians! For tool / bronze rush. The fast-firing archers are epic.
Minoans, because they only do one thing right (Composite Bowman + Centurions) but they have all the right bonii to make it work.
This is how I wish more civs played like.