What can I say... my hands hurt. I've been playing on the Xbox 360 almost all day. I haven't been this into gaming since the Super NES days. (Sidebar: I realized while talking to a friend that the first two things I ever bought with a credit card were a TV and a video game console, the SNES. Weird how history repeats itself.)
I also picked up NBA 2k6 and Project Gotham Racing 3, so I more or less have four game genres covered. All four games are awesome. I spent quality time playing them on Xbox Live too, and that is where these things really shine.
While playing a really simple track on PGR3, I was talking with a couple of guys about where they found their 360 machines, and was surprised to find they were also "got lucky" customers like I was. And that's what's so f'ing cool but this live stuff, that you can talk to someone anywhere in the world about dumb shit like this as if you're in the next room. And given the price of the box and the rising age of even hardcore gamers, they're adults.
That's not to say you don't have some real funny moments too. I was deathmatching on Perfect Dark Zero (always a ton of people on!), and I heard some guy (or kid) yell, "Ownage!" Come on, seriously... nobody really says that! Alas, I made it my mission to kill him, and I did so twice. Otherwise I was mostly getting my ass kicked, but laughing every time someone sent a rocket at my head. Death and destruction can be funny.
I played a couple of rounds of Joust with people too. There's something I wouldn't have thought of, that a game two decades old could find new life by way of online play.
So while there are amazing games for the Xbox 360, what really makes it amazing is the live service. Microsoft really, really got it right. All of the haters need to get over it... this thing is the shit. I just hope they can catch up with demand quickly because it really is an amazing experience to share with others.
Do it. The 360 is THE shit. The Live integration is just amazing. My brother and I got ours launch day (preordered months ago), and spent hours that evening chatting in Live while playing various games. Not even always the same game -- the integration is that good, we were each able to go to other games without dropping the chat. You COULD accomplish the same thing with a phone, or on a PC with Skype, but it's all right there, and dead-simple to use.