Free for all, Team slayer, CTF, Assault (carry a bomb to the base and arm it), oddball (carry a ball around - each team either defends the ball carrier or attacks and tries to get it back, the person holding the ball gets points for the team [or himself if its free for all]) and king of the hill are the main ones (but there are plenty of others) the possibilities are endless really. There are literally dozens of different combinations and throw in a few vehicles and the gameplay changes dramatically.
There is even a new feature where you can change everything on the map on the fly - spawn points, weapon spawn points and loads of other stuff (still dont know much else about it myself yet) best described as similar to Garrys Mod for Half-life 2, but you can actually play your game types such as CTF etc on it as well while being able to edit stuff. The customization options are far, far more indepth then GRAW so you can create any game type you can think of really.
Halo is very playable, probably one of the easiest games to pick up and play just dont be expecting to jump straight in and get loads of kills against some of us whom have been playing for years (I know you're not but loads of people make that mistake and eventually get sick of dying and stop playing, all Im saying is give it a chance).
Also Forgot to mention it has 4 player co-op over Xbox Live, yes I know you hate the single player but if its with 3 mates it can be a great laugh and should show Gears of War how its meant to be done

I can play Halo either with friends or on my own in matchmaking which is why I love it so much, no waiting around for a game if your friends arent online

and Halo 3 is taking elements from both Halo 1 and Halo 2 to make it the best one yet.
All I can say is give it a week or two and make up your own mind. The best way to describe Halo is its not really innovative and it takes things from all the best shooters around and brings them together in one very well polished package.