I thought my Core 2 Duo machine was 64-bit. I’ll have to look at it a bit more. After looking around I found the version package which very easily tells you what version you’re running of various programs. Just enter version program-name or version ubuntu or version kernel to check what version of a program, ubuntu, or the Linux kernel you’re running, respectively.

Using the last option showed me that I’m running it in 32-bit mode right now.

Get it from http://programs.rcrnet.net/#version