I’ve just installed Windows 7 on an old computer to see if it could be done.
The installation is large enough that it requires a DVD, and a DVD drive. The only problem with that is that older computer generally cant boot from a DVD.
Windows 7 was designed to be installed on top of (or beside) an existing operating system, one that has DVD drivers already loaded.
To get around this limitation, I found it was possible to use a Vista Repair Disk that Microsoft provides. It has the bootloader and DVD drivers necessary to load Windows from the DVD.
My Windows 7 installation is running on an AMD Athlon 1.1 Ghz cpu, with 1GB of RAM and a Radeon 9550 video card.