Depends on the OS you're running. If you're running 32-bit Windows, 1GB is the absolute minimum, with 2GB the "recommended", but you'll see better performance with 4GB.
If you're running 64-bit Windows, 2GB is the minimum to run...kind of like you could "run" Windows XP on 128MB (but it ran much better on 256 or even 512MB). 4GB is really the true "minimum" to get any kind of decent performance, and 8GB would be preferable.