It depends on the PSU really.
If your system wasn't built as a gaming machine, there's a good chance that your PSU will be some crappy generic piece of tat that's not really going to be well suited to feeding a decent graphics card.
My system, for example, only came with a GeForce GT 420, which isn't designed for gaming (runs Dead Island on high setting pretty well, but cries at the thought of running games like Champions Online or Deus Ex: HR with anything near), but the rest of my system is fairly decent (2.8Ghz i5 with 6GiB of DDR3).
Because it's not powering a good graphics card, my PSU is some weedy little box of crap that only pumps out around 250W, which isn't enough to power, say, an AMD Radeon 6850, which needs at least a 500W PSU.
Your best bet would be to open your system, find out how much power your PSU can pump out and what connectors it has.
Also, while I'm here...
Does anyone know if the XFX AMD Radeon 6850 or 6870 are any good?
I'm planning on buying a new graphics card and PSU between now and early 2012, but I don't want to spend more than about £200-£210 on the graphics card and £70 on the PSU.
Also, yes, I know about AMD's iffy numbering system (6870 is below 5870 and such).
I say they look more like german/caveman then asians.
The Germans are coming to beat you with clubs and spears!
Hundley: Damnit kid, get off my lawn!
Faust: NOT UNTIL YOU GIVE MY MY PANTS BACK HUNDLEY!