According to IGN, Microsoft has revealed that the Xbox 360 will not be compatible with peripherals from the current Xbox. This really shouldn't cause too much of a problem, however, as the 360 controller features almost the same layout (the black/white buttons would have to be remapped to two of the shoulder buttons). The main drawback here is that to play Halo, Halo 2, etc. on your 360 you'd have to buy 4 360 controllers.
Of course, this doesn't mean that some 3rd party companies won't develop an Xbox -> USB converter that will allow your Xbox controllers to function on the Xbox 360.
Source: IGN
Of course, this doesn't mean that some 3rd party companies won't develop an Xbox -> USB converter that will allow your Xbox controllers to function on the Xbox 360.
Source: IGN