The Xbox One will NOT be compatible with the 360.
Though the Xbox One is here, it might be a wise move to hang onto your 360 if you plan on playing any of your old games. Microsoft's Xbox Live VP Marc Whitten recently confirmed to The Verge that the One will not be backwards compatible with the 360. "The system is based on a different core architecture, so back-compat doesn't really work from that perspective," he stated.
Yes, this goes for Xbox games on disc and current XBLA titles. Since the Xbox One will be packing an x86 CPU, it'll be wholly incompatible with the games designed for the Xbox 360, which packs a Xenon processor. Though Sony's PS4 will also face the same issues as the PS3, Sony will be bringing PS3 games to the PS4 from the cloud. Unfortunately, it doesn't appear that Microsoft will do the same thing. "When we specifically asked Whitten whether the company had any streaming option or download option for existing Xbox 360 games for the Xbox One," wrote The Verge's Sean Hollister, "he confirmed that there was no such thing in the works at Microsoft."
So it might not be the best idea to get rid of the old and replace it with the new...