There has been much speculation on whether the Xbox will be backward compatible. Reuters says “yes”:

Microsoft Corp. said on Monday its new Xbox 360 will run video games developed for the earlier generation of its gaming machine, an enticement to get fans who have already spent hundreds of dollars on older Xbox games to purchase new hardware.

Shacknews says “somewhat”:

Xbox 360 will have limited backward compatability. Only the most popular Xbox games will be supported, through an emulator.