The most comprehensive guide to outlining the steps on what to do to find out is provided by Microsoft, located on their website under : http://support.microsoft.com/kb/827218/?FR=1 , but here's a cheat-sheet version to keep handy! 
XP or Windows Server 2003
- Click Start>Run
- Type sysdm.cpl . Click OK
- Click the General tab.
- Look at the operating system.
If the operating system has an x64 in it, then you are running a 64-bit version. If you do NOT see this, you are running the 32-bit version.
Vista
- Click Start. Type system in the Start Search box.
- Click system in the Programs list.
- Look at the operating system.
The System type under System value will show either 64-bit or 32-bit.