I've been trolling this board, picking up tips, since I got the game and this is my first post.
I voted for "Ancient Age", even though I just recently learned that this was an excellent way to win (a few weeks ago I would have voted for "only when I get attacked" or "only Modern after tanks").
I used to go to war only when I was attacked, preferring to be a peaceful builder during most of the game. This works fine for Civ 1 and II, especially on the easier levels (ok, I've been playing Civ since it's inception and I'm only now getting good enough to play it at the Monarch and above difficulties). However, in Civ 3 it's very difficult to keep up with the Jones' using this path, even on Warlord. So I discovered what most, if not all, the good players do. Start a war early. Get all the other civs you know to ally with you against a single foe and beat the tar out of them. Rinse and repeat as often as you can afford. In my [limited] experience, it helps to have a large army as allies are easier to pay off.
I've been playing the Chinese in my latest game on a large map with 3 smallish continents and 1 large one (might be more land because I haven't fully explored - it's about 1100 AD and I just found 2 continents which are each capable of holding at least 5-10 cities each but have no settlements). I've managed to wipe out the Iriqouis (only civ that started with me on my small continent), then the British (with the help of the Japanese, Americans, Romans, French and Babylonians), then the Japanese (cuz they broke a treaty with me to fight the British-all above helped), then the Babs (cuz they wouldn't help me beat up the Japanese -- all but French helped), then the French (cuz they had the other half of the Babs continent -- did it myself in 3 turns). All before 500 AD and all with every other known civ (I'd pay them off with as little money as I could and usually a ROP). The result? By keeping everyone at war early, I managed to take alot of land (I now have about 50% of all the land I can see) and a huge tech lead (I'm playing Warlord). Now, I have complete control of 2 smaller continents (with 8 - 10 cities each), just finishing wiping out the Romans [they're technically still alive because they have a trireme somewhere, not sure where] and 60% control of the main continent (America has the rest). I've recently discovered the technologically backward Egyptians and Germans (who were too far away from anyone else due to oceans) and they don't know about the Americans. I'm building up my forces to crush the Americans (my biggest threat, because they're so close and they have a large army) before they meet Egypt or Germany. With any luck, I'll win by domination (will be my first time) by 1500 AD and prove to myself that early war's are really awesome.