You're going to have some fun gaming.

I didn't get mine that long ago (just after Easter) and I think it was worth it. There are some pretty cool games. Gears of War isn't that bad, mind you, I've only played it 2-player (my sister likes playing co-op with me). Though it is just all muscle, sweat and blood when you come to think about it. I bought it to check out what the fan-boyish is all about, it's not for everyone though.
Anyway, my recommendations:
Fable II - I was recommended this and I loved it. Though it's short it's worth every penny - I even formed an emotional attachment to some of the characters, like my dog, wife and daughter.
Halo 3 - another game I bought to see what the fan-boyism was about, it's actually a very fun game, it's interesting too, though it seems you need to play Halo and Halo 2 to know what's going on. I've been confused mostly trying to pick up what's happening as I've been going along.
Mass Effect - A very good game - I had to buy it again for the 360 because the PC version was too buggy. This is one of those games you'll need to install to your hard drive to get better loading performance, which you'll need. Very interesting story, and I love the interactivity with the characters and how you can effect the outcomes differently by how you act or what you say. It is a 3rd person shooter with RPG elements (you even level up)
Fallout 3
If you're into Japanese RPGs (which the 360 has a good selection of), I recommend:
Star Ocean 4 - some characters are annoying and voice acting is poor. Get your head around it and
you've got yourself an additive games with an interesting storyline. The battle is real-time, no random encounters. This game can have you playing for many hours, I'm nearing 40 hours, without doing side stuff.
Lost Odyssey - a must have JRPG, it's turn-based with random encounters, the system will remind you very much of the Final Fantasy games because it's by one of the people who made the Final Fantasy games (I believe the originals) and the music is by Nobuo, who is a very good game music composer I think. This will have you playing for many hours too, I'm stepping over 30, without doing side stuff. The has some quite emotional moments in it - certainly it tries to have a heart moving story.
Infinite Undiscovery - It's interesting, it's by the same team as Star Ocean 4 - and I've enjoyed it so far. It is real time battle.
The Last Remnant - I have it for the PC, but the battle system is turnbased, though there's no random encounters. Instead of individual players you have factions in the battle. It's a little different by that respect. It's by Square-Enix and I though it was really good, I quite liked the plot and enjoyed the ending. The difficulty is unbalanced, so there are some unnaturally hard bosses and you can feel them to be a bit cruel, like the Gates of Hell, who raises dead characters and makes them attack you. On the 360 there are meant to be a few bits that aren't optimised properly - it's supposed to be better if you install it.