In my opinion the Xbox 360 is the console of this generation. It has a large library of quality games and through the wonders of Xbox Live you also have access to a lot of great, smaller games like Braid (which is also available through Impulse) and re-releases of games such as Banjo-Kazooie and even some Xbox Originals. And, of course, the downloadable content, which is becoming one of the 360's best selling points. It also does other great things besides games - it supports iPods and iPhones to stream your music collection for example.
The only real problem I have with the Xbox 360 is you pay for everything. Downloadable content always costs and most backgrounds and gamer pics cost. While it's not very expensive, it's annoying to pay for things you get for free on the computer. If your like me though, you'll only get the DLC for your favourite games.
Another thing worth mentioning is if you live outside of North America you might experience some issues with Xbox Live. I, for example, am simply unable to play over Xbox Live due to both NAT issues as well as Ping issues. Match Making simply dumps every player into a pool and picks out players at random. Very few games allow Match Making by location, so getting a game where everyone has acceptable Ping levels can be very problematic. For me, it was a deal breaker and I won't be renewing my Xbox Live subscription.
Apart from that though, I've had the Red Ring of Death problem, got a free replacement Xbox 360 within 7 days as well, and I still have to recommend it. It's a great console with great games.