I've gotten the three rings once, and I was actually pretty surprised with the service Microsoft provided. I called them, and within a week a cardboard-coffin arrived, and I packed up my 360 and shipped it out (shipping was paid for by MS). Two weeks passed and my 360 came back, good as new. MS also sent me a gift card for one month free of Xbox Live, to make up for the 3 weeks I lost on my subscription. Not really a bad deal, and everything was free. Its been running flawlessly since I got it back.
Most of my friends have 360s (I'd say around 10 or so) and myself and one other person are they only ones who have run into problems (we've had ours since the systems release, so it seems older consoles are more prone to the 3 Rings). If you're going to get a 360, try to find out when it was manufactured before you purchase one. If you're getting a console, 360 really is the way to go, because it's a console. It's not a home entertainment system like the PS3 claims to be, and it isn't trying to be super innovative with motion sensor controls like the Wii. The 360 falls somewhere in the middle, and I like everything about mine.