Couple months ago, my ol' PSU died. I tried an older one I found in a machine that was just laying around, a generic 250w/+12v@10a. My system specs being: X2 3800, E-7600gt CO, 2gb's of Pc-3200, 2 HDD's etc. What the hell, if it didn't work, nothing off my shoulder, as JLV2k5 stated if it isn't enough it just won't operate. It did work though, and I tested it further too, I could play all my games just fine, I used it normally as if the low current/wattage PSU was nothing. the only odd thing that happened was the video card temps rose just a bit.
It only restarted once in the 1 and a half week period i used it, and that was after I attempted overclocking it to my regular level. So if in doubt, give it a try, you never know.