The easiest way to tell is to check if you are running Windows XP – Home, Professional, Media Center or Tablet PC Edition version 2002 (or Media Center 2004), you have a 32bit version of Windows. At present the 64bit Editions of Windows are packaged with 64 Bit computers and the client versions are packaged with the name '64-Bit Edition' or 'x64 Professional' rather than just Home or Professional.
If you don't know what package you have, and you know windows registry, you can then open up the registry (regedit): "HKLM\\SYSTEM\\CurrentControlSet\\Control\\Session Manager\\Environment\\PROCESSOR_ARCHITECTURE".
If the value is "x86", then you have a 32 bit version of Windows. Otherwise, your Processor Architecture is not 32-Bit x86. Your machine could be potentially running a 64-Bit Edition of Windows. You should open your system properties to identify which hotfixes to apply on this system.
Intel Itanium/II CPU = patches marked IA64 AMD Opteron or Athlon64/FX = Patches marked as AMD64.
There are some other ways. On Windows XP or Server 2003, you can try command "sysdm.cpl". On the General tab, under System, a 64-bit version operating system should include "x64" in the name, for example, "Microsoft Windows XP Professional x64 Edition Version < Year>".
Or you can try command "winmsd", in the details pane, locate Processor under Item. If the value that corresponds to Processor starts with x86, the computer is running a 32-bit version of the Windows operating system. Otherwise, it starts with EM64T or ia64 for a 64-bit version.
Check on How to determine whether your computer is running a 32-bit version or a 64-bit version of the Windows operating system
for Windows Vista.