Some of us need to install XNA Game Studio — but we’re not using Windows Vista or Windows 7; in fact, we’re on (aging) Windows XP — and 32-bit XP, of all things. For example, I use Flat Red Ball for Deen Games development. FRB is built upon the XNA API.
If you try installing XNA 3.1, XNA 4.0, or the redistributables, you’ll get an error; likely because the EXEs weren’t made for your OS and CPU architecture.
So what do we do?
This post by Travis Gockel makes it easy; he’s dug into the Microsoft site to find the 32-bit XNA installer, and linked that (as well as prudently uploading it onto his own server).
You can find the download from his page; the MSDN page he referenced is here.