As I'm sure most of us know, the original 360s had an extremely high failure rate and were prone to overheat and flash the RROD (red ring of death) at any given moment. Have you ever experienced an RROD or other 360 system failure? I'm one of the lucky ones, I guess. I've had my 360 since August 2008 and I've never had any type of failure.
My original 360 (Bought in November of 2008, now owned by my brother) has never gotten the RRoD. As for the 360 I own now (I don't know when it was bought, but it's one of the older, non-Slim or Arcade models), it's never given me any problems. I have a friend who's gotten the RRoD on his 360 at least two times, though.
I got my 360 in umm... February 2008, I think, and it's RRoD'd on me once. It was last year in May and I sent my console in and within a week had a refurbished replacement. Except the replacement had scratches all over it that I thought would bother the hell out of me. I was kind of outraged but couldn't open a support ticket right away (it was advised by their twitter team) since it hadn't registered that my previous ticket was finished with and by the time I remembered later, it had been so long that I figured it would be too much of a hassle to prove I hadn't just been an idiot and scratched up my own console. And I guess it hasn't been that noticeable, though whenever I move the console (which is surprisingly often), I can see and feel it and that bothers me. But it works fine, so I guess things could be worse. :/
I got the red ring of death a couple of years ago. Luckily all I had to do was send it in and they gave me a new one for free. They also gave me a free 1 month Xbox Live membership. All of the new Xboxs will not have the Red Ring of Death, at least that is what Microsoft said. However I think that getting the RRoD nowadays is rare.
I experienced it on my original Xbox 360 arcade edition. I never got it fixed because I was too lazy to send it in and didn't care much about it because I was playing basketball in school.
I got the RROD once with one of the older consoles, I actually remember a friend of mine whom I game online with, he got a RROD and even though we knew he shouldn't have done he kept his console on with the RROD and we played terrorist hunt on R6V2, could see everything as it all came up on his screen like a heat screen, managed to beat one map we was struggling on thanks to the RROD :) never had RROD since I got a new slim line Xbox 360 though.