As yokozuna said, most programs designed for Windows XP will also run in Windows 7. However, there are several that will not run, or will not behave properly if they do manage to start. However, with Windows 7 Professional or Ultimate editions, one can download and run "Windows XP Mode" which allows any Windows XP program to be run in a virtual XP environment. The download is available here and is free as long as you already have 7 Ultimate or Professional edition.
Select as Best AnswerUndo Best Answer
Look up your app on the Windows Compatibility web site: http://www.microsoft.com/windows/compatibility/windows-7/en-us/ Most apps will work but keep in mind that some apps will only work on Win 7 32-bit but not Win 7 64-bit (e.g. Medieval II Total War). If you are looking to upgrade a current installation you can run the scan (bottom of the page linked above) and it will tell you if any of your currently installed hardware or software will not work with Win 7.
It depends on the program. Most will, but a few won't. I learned the hard way when my edition of Adobe Premiere would install but not run. Google your particular program and see what you can find in forums. If you can't find anything, chances are that it's good to go.