YES!!
But first: There is now a HUGE selection** of native Linux SW--some of which is BETTER than the Windows equivalent.
To run Windows programs on Linux, you would use a program called "WINE"---or the commercial version: "CrossOver" (WINE with a friendly interface)
There is now a pretty large selection of Windows programs that work very well on Linux. As I write this, I have MS Office 2007 running on my Arch system, and it is essentially perfect.
There is a very good compatibility list at the CrossOver site:
http://codeweavers.com
**I have a hunch (untested) that there is now more SW available for Linux than for Windows. This of course proves.........absolutely nothing.