Yes you will be able to run you Windows XP probrams.

Windows 7 offers Windows XP Mode which is specifically designed to help small businesses move to Windows 7. Windows XP Mode provides you with the ability to run many older applications on a Windows 7 based PC.

You need to install these applications directly in Windows XP Mode which is a virtual Windows XP environment running under Windows Virtual PC. The applications will be published to the Windows 7 desktop and then you can run them directly from Windows 7.

Windows XP Mode and Windows Virtual PC usually recuire an upgraded Windows 7 PC. Windows XP Mode and Windows Virtual PC for Windows 7 are only available in the Professional and Windows 7 Ultimate packages.

Most of the programs working on XP is working on 7.
However, there are some very old programs that are working on XP is not working on 7.
Virtual PC and Windows XP Mode is one of the to overcome this problem as long as the hardware on your PC can support Virtual PC (Virtualization Enabled Processor). Besides, only Windows 7 Ultimate can support Virtual PC

You can log on to this site to check if programs in your PC can work on 7 before upgrading:
http://www.microsoft.com/windows/compatibility/windows-7/en-us/default.aspx