Race. If you want to win, don’t try killing people unless they are really in your way; it just wastes time, and sometimes respawns people closer to their waypoint. Know the map and know the track so you can easily and quickly get from one waypoint to the next. If you get ahead of the pack early on you have a better chance of winning. I find adding respawn time growth of 10 seconds or 5 seconds makes race games more violent, if you go for that sort of thing; people have more of a motivation to kill each other that way. Good race maps are Blood Gulch, Wizard, Rat Race, Battle Creek, Damnation and maybe Derelict.
Team Race: Remember everyone on your team has to complete the laps. If you complete them early on it may be a good idea to either camp at a waypoint or escort the players who don’t have any waypoints. Sticking together is sometimes a good idea for team mates but usually very hard to do. Splitting up and getting a player to complete a lap early on so they can help later is a better strategy. 
Rally: Don’t go chasing after every single rally point; you’ll probably get stuck in the middle of them. I find camping in an area with a few nearby waypoints can win the game (of course that depends a little on luck too). 
Team Rally: Again remember that all the team members have to get 3 flags. You may be better off letting one player at a time get the rally point. Defend the position until they can get there and get the flag if you can. Don’t be too greedy; if a players ends first, they can camp waypoints better later.

King of the Hill. You may want to let your opponents duke it out before getting on the hill (unless they are ahead). Get to the hill quickly. Remember that you can still accrue hill time while in a vehicle. Sometimes it's helpful to get off the hill to ambush an opponent. Get grenades if at all possible before going to the hill; they are quite handy.
Team King: You only need one team member on the hill to score and having more doesn’t help your score. Having some players roam and intercept incoming players can alleviate a lot of stress at the hill.
Crazy King: Some hills can be easier to defend than others. Hills spawn in different spots every minute.

Oddball.  Find a defensive position and take the ball there. Use explosions to move the ball around quickly; this can be useful to get the ball down from high places, or to punt the ball away from opponents or towards yourself. Throwing the ball at your opponent can sometimes be good; they have to fumble a little to shoot at you, and in the meantime you pump them full of lead. The weapon you're carrying when you pick up the ball is the weapon you'll grab when you drop it, so choose your weapon carefully. Remember you can melee with the ball; two hits will kill an opponent. You won’t score time while driving or gunning vehicles when you have the ball, but it's still sometimes useful.
Team Ball: Ball control is important; if your team has the ball you spawn close to your teammates.
Reverse Tag
Accumulate: Get several kills in a row, then camp - your time counts faster the more kills you get in a row.
Juggernaut: Can be good on Boarding Action. Make sure you are well armed when you become the juggernaut. 

Slayer. Good slayer maps: The smaller maps and arena maps are better slayer maps, but all are pretty good. The best are Chill Out and Damnation I think.  
Slayer
Team Slayer
Slayer Pro
Elimination
Phantoms
Endurance
Rockets: Good on Derelict and Longest 
Snipers: Good on Hang 'em High, Sidewinder and Prisoner.

Other Settings. No shields, 50% health, pistols Slayer game. If you like one-shot/one-kill and fast-paced games, give this a try. Play to at least 25 kills probably.
Single flag CTF. Very different strategies than regular CTF games.
Moving hill, hill in motion tracker. Kind of a scavenger hunt. Can be fun on the larger maps with vehicles. Might want to make time to win 5 minutes.
Try out the different vehicle sets on the vehicle maps.
Ghost race on Blood Gulch, repsawn time 10 seconds, respawn time growth 5 seconds.
No shields 200% health: Same amount of overall health, different ballgame all together.
Multi-ball juggernaut ball: The player who kills the most juggernauts can corner all the balls on the map. The oddball settings are the deepest and most versatile; play around with different traits with and without the ball.
Try some team race; that way not all team members have to perform laps and some can play more defensively.
Weapon sets will replace weapons; this includes your starting equipment. Different weapon sets can really change a game's strategy.
War: 400% health, all weapons, one life, Capture the Flag. Fun with lots of players.
Try playing some games without the motion tracker; just set the other players on radar to no.

If you want something a little silly try an invisible players team game without friendly indicators. If you really want to see chaos, try this with 50% health.