Dumb question, but how do you check if you have the 64-bit or the 32-bit version of Windows XP?

Oh dear. You should know which OS you're using without having to find out =/

Rclick on My Computer, click Properties. Hopefully it'll say if you're using XP x64.

If all else fails, try installing something 64-bit and see if it fails miserably.

Well, I thought I knew this. I've been having weird errors both ways. I always assumed that right clicking my computer/properties would tell you. Mine doesn't say x64, so I always assumed that I had 32 bit. But a few months ago I tried to download and run an official Oblivion mod, and it wouldn't work. The elder scrolls site says that this error only occurs on 64-bit machines.

It's not been an issue since then, as I wasn't -dying- to play the mods. But now I'm trying to update my drivers, and I needed to know what OS I was on before doing that. I was pretty sure that I was on 32-bit, but the confusion with the mods not working had me doubting it.

Thanks for the help though, installing drivers now.

The properties will tell you, like Xinael said. If you are running 64-bit, the second line under System will just say 'Professional," if you're running 64-bit it will say 'Professional x64 Edition'

If for some reason that doesn't tell you, then in system properties go to the Advanced Tab, click on environment variables and under system variables there should be an entry called "processor_architecture".
x86 is 32bit
AMD64 or EMT64 is 64bit.

Usually your Program Files is called 'Program Filesx86' as well.