Erm, a X600 is fine, maybe up to X850. If it's the system I see, that'll work. Although, I don't know about my PSU, but I know I run an 8500Gt. Nothing too hardcore.
Look on the side of your power supply and tell us how many amps are on the 12V rail. This is needed to determine what your PSU can handle. Also what brand and model is it?
Maybe I'll get a new PSU so I can have a real good graphics cards!!! Thing is, I think my current PSU is a uATX/BTX!!!! Is there one around that cant hit 500W???
To be sure that an 8600GT will run fine with you PSU, please post the brand and model so I can find the 12V rail specs for it. Don't buy your new card just yet.