Hey, if you morons like fighting games, get Virtua Fighter 5, it's supposedly the best 3D fighter in years. I don't usually play the genre, but the game is pretty awesome. If you meant beat-em-ups, XBLA has at least a decent selection from old arcade/console titles.
I agree with space games. There needs to be a space sim (that uses the Ace Combat 6 flightstick). Maybe if Lucasarts wasn't a steaming pile of Hades nowadays, we'd get something. Or a mech sim. Like Steel Battalion 2 ^___^
We need to play more NHL 2008 co-op.
If you guys like board games, you should try Catan (XBLA). I have the real board version, and it's pretty nice (economy/trading-based). If it doesn't turn out to be the free game, it might be something worth getting, if we're all willing to invest in it.
Also, try the Culdcept Saga (will be a budget-priced retail game - not XBLA). It's a mix of Monopoly and M:TG (or whatever other card game). It's awesome.
You guys should also try Puzzle Quest (XBLA). It's a mix of Hexic with RPG elements, and it works masterfully. Arguably one of the best games last year. There's also 1v1 online. I don't have it since I already have the DS version, but Nick has it.
The beauty of Live is that you can just simply try the demos of all these games.