Simple strategies (playing at Regent). May be obvious to you but I just clued into them in the last week or so :
** Worker keyboard short cuts : shift-p will have worker zip directly to pollution and start cleaning up. shift-j will have them seek out + cut down jungles until all the jungles are gone from your territory. ctrl-a (command-a on macintosh), then click a tile will have them build a road or railroad from point a to point b. shift-a will automate but they won't destroy existing improvements.
** If an AI civ declares war on you out of the blue, before you are ready for it, _immediately_ go to the diplomacy screen and contact every other civ in the game. If you're strong and have a decent rep, you can get them into a military alliance (meaning they will declare war on the aggressor immediately) without trading them anything for it. Don't forget to ask for trade embargoes as well. Now, wait a couple of turns and if possible take a city or two from the aggressor. Sue for peace. The other AI civs will continue to wage war against the aggressor civ -- usually if for a long, long time. You won't get dragged back into it because you never signed an mutual protection pact with anybody. Even if they other civs sign peace treaties, those trade embargoes you signed will probably last 20 turns, so that agressor civ won't be able to trade anything with anybody for awhile at the very least. Every time I've done this, the aggressor civ has either been wiped off the map or severely crippled. It's also a great way to play the AI civs off one other.
** You can egg AI civs into declaring war on you. Go to the diplomacy screen every turn and demand that they give you one of their top cities. They'll keep saying no, no, no and get more and more annoyed, eventually declaring war. Doing this gives you a war weariness and rep bonus -- you get less of a hit if you are not technically the invader/aggressor.
** Slap around bordering civs early in the game (see Rear Admiral's post early on). You can cripple the AI's expansion, and sue for peace in 1 or 2 turns (usually before they show up with units to retake their capital/city). During the negotiation, you can almost always to get them to give you all their techs, gold, and extra workers. I've done this many times and it always works. Note that some civs (England, Germany) will carry grudges and won't talk to you if you do this. Also, you risk taking a rep hit for a loooong time.
** Civs in your culture group will be friendlier and more willing to cut you deals in the diplomacy screen. For instance, if you're the Egyptians, then the Romans and Greeks are your buds. For the Americans, it's the Iroqois and Aztecs, etc etc. Work this to your advantage when you can. Of course, they also might be near you at the start of the game, so if you take the advice from the point above and slap them around, this won't hold true.
** Ghandi requires no strategic resources to build his special unit, the War Elephant. Slap him around before he starts building them, because, as was pointed out previously, Ghandi is a prick.
PS: I just spent the last couple of hours reading through all 19 pages of tips. Thanks to everyone who posted. Very helpful all around! And cheers to other Civ addicts who are still reading these tips, 19 pages later in the middle of the night ...
I'm glad you have taken a civil attitude toward my comments, even though I was exasperated and 
SO i can't play as much as i'd like to either... So enjoy whatever level you play on, and as the games become to easy, move on up 
