I found (On my system at least, an HP Desktop (x64 with an AMD chip) bought last summer) the latest version of VirtualBox would run the 32 bit version of Windows 8 (Or at least install, that's what it's doing now) once I enabled virtualization in the BIOS. So, for people having VM issues, perhaps check your BIOS to see if you have some virtualization setting disabled as I did? Though be sure you know what you are doing or you may mess something up on your system, such as boot order and whatnot.

Edit: Like Stinomus said above, when you are creating the virtual machine make sure to set it to Windows 7, rather than Windows Other as I did originally.