Hamed Mokhtar was kind enough to submit some helpful hints for Civ3. Try them out and let me know how you do! And if you have some tips of your own, send them in.

1. Select at least a Large Map.
   If you’re computer is a bit slow however, stay away from the Huge maps because it can bog down a slow CPU.
2. Make sure and choose the maximum number of other Civs. Chances are they’ll beat up each other instead of you.
3. Choose a Scientific or Religious civilization coupled with Industriousness. You want to start building culture in your cities ASAP. A scientific or religious civilization can build either Temples or Libraries quickly. This will give you an early edge in cultural expansion and give an overall boost to production.
4. Go for the Golden Age wonders! If you can get a Golden Age you will have a massive production and scientific advantage. Religious civilizations may get a Golden Age from building the Pyramids. So if you want an early lead, this is the way to go.
5. Make sure and trade your excess resources with other civilizations. But not for Gold. Always try and get science advances. Science production will benefit you more in the long run.
6. Never trade away science advancements that give world wonders unless you’ve already built it. However, a good trick on this is to wait until your almost done and then trade the science away. Typically any science advancement that leads to a world wonder will be quite sought after, so you may be able to get two or three other advancements in exchange.
7. Don’t forget to build an Army. A high culture isn’t quite enough to keep your would-be enemies at bay. A good military backing can be a tremendous boost to your negotiations. You’ll be surprised how nice other civs are when there’s an Army or two parked in your cities.
8. Don’t start a major war until you have the Tank. You want this BEFORE your opponents. The tank can literally run over everyone. Of course if you picked Germany then build Panzers ASAP. This basically means you have to go deliver some serious beat-down to another unfortunate Civ.
9. Make your wars quick! Build up a force and try to take out the other Civ in about 5 turns. If they have cities on another continent, make sure you make peace with them. Long drawn out wars will cause war-weariness in your cities and that will be bad. But, short quick wars will actually cause your people to love you and build additions to your palace!
10. Get the Great Library at all costs! Even if you’ve managed to keep ahead of everyone else in Scientific research, you need to keep the Great Library out of everyone else’s hands. If you can’t pull this off, you need to seriously consider restarting.
11. Do whatever it takes to get a Golden Age no matter what time point in the game. You will always reap major reward by doing so.
12. It’s a good idea to keep a Leader around to hurry production in case you need it. Even though you might be tempted to build an Army with him, having that Leader around is an ‘ace in the hole’ should you find yourself just shy of a very critical goal.