Bad news for those who have a large Xbox 360 game library: the new Xbox One will not feature backwards compatibility for Xbox 360 games. According to Xbox Live VP Marc Whitten, there will be zero backwards compatibility, mostly due to the fact that the architectures are completely different.
No, there's not. The system is based on a different core architecture, so back-compat doesn't really work from that perspective.
Not only will Xbox 360 discs not work, any Xbox Live Arcade game built for the Xbox 360 will need to be rebuilt to support the new platform. However, the Xbox One will support many titles from the original Xbox through emulation. Furthermore, Microsoft has no plans of discontinuing the Xbox 360 meaning you'll be able to buy a new one should yours break for the foreseeable future.