Transfering purchases between consoles

So 2 weeks ago, my xbox 360 had red rings, after I had left it on all night. I turned it off, turned it on and it fixed it. Went to the dashboard. But that scared the crap out of me and made me think, if my xbox fried, and I bought a new one, would I be able to transfer all of the games I've bought? Providing that I use the same profile and all?

If you use the same Xbox Live account you should be able to download the games again for free or you could get a transfer cable.

took you that long to get the rings? lucky you. PS Xbox One has so much less fault rate. I read no where regards machine stopping. Microsoft finally has built a good system