Can I run Microsoft Money on the Xbox and Xbox 360
Simply put, no.
The Xbox and Xbox 360 have been designed as gaming machines and do not run productivity applications. In the case of the latter (Xbox360), this actually uses PowerPC processors which means the code for Microsoft Money will not operate as it is designed for Intel processors.
The roadmap for Microsoft's Xbox devices does not specify whether it will evolve to run other applications apart from games and a Media Center front end, but with a gaming handset, putting those numbers in will be tricky ;-)