Yes, they will. There will be some exceptions, of course, especially
programs that involve a more nitty gritty interaction with the system e.g.
anti-virus programs, system utilities etc.
Windows 7 will come with a "Compatibility Mode" which enables you to run
programs "as if" they were running on another version of Windows e.g.
Windows 2000 or Windows XP.
Furthermore, Windows 7 Professional (but not Home or Basic) will include a
somewhat integrated Windows XP virtual machine - business applications that
need Windows XP will be able to run on the Windows XP virtual machine (which
runs on top of Windows 7, of course).
To sum up, with rare exceptions, programs that run on Windows XP will run on
Windows 7 one way or another (natively or natively in Compatibility Mode ..
or on an integrated virtual machine (XP)).
Saucy