256 is the bare min most of us would recommend. I say 512 at least.
Sure it will run on 128 MB, but it will be very slow. And that is assumming you dont want to run games or office or anything fancy.
I did a migration last year for a large company, they where initially using 128 Mb machines to run windows XP. After a slew of user complaints due to the SLOWNESS of it all, they made a large order of 256 MB dimm to add to all the other machines to speed things up.
It save me about an hour per machine setting up stuff.
suffice to say you want 512 MB if you plan to play games like warcraft 3, UT2k3, UII, etc.
256 mb will still feel slugish has well