I usually start a game with a particular strategy in mind - all war, aggressive, peaceful, isolationist, peace-keeper, etc. I usually play peacefully - which rather sucks in Civ 3, since they made it pro-warmongering.
Although, I do have a few triggers:
1) Raze a city I founded - I raze ALL of yours. (conquered cities aren't my people, so I tend to only treat as a normal war in that case).
2) Nuke a city I founded - I nuke ALL of yours.
3) Sneak Attack me - I play like Civ2 - TREACHERY! War until one of us dies!
4) Burn London to the ground - TO THE GROUND! (cuz Scotland is free)
5) I usually have a "buddy" Civ that I will back up as long as I can (though they often declare war on me eventually - hope that's resolved in Civ4)
Otherwise, I war, I peace, but mainly - I just try to win.