Can my power supply run my video card?
Power supplies and video cards are two fields rife with estimations, guesses, and even outright lies. Bringing the two together, as you might guess, does not always produce positive results.
Modern video cards often list a power supply "requirement". They "require" a 350 W power supply, for instance. Unfortunately, the truth is that this is a complete blind guess on the card-maker's part. The idea is to specify something with enough overhead that even a fairly bad one is likely to be able to handle the card and a typical computer.
So the number is fabricated. And worse, it's based on other numbers that are sometimes fabricated. Many power supply companies are less than perfectly honest. Even when they're honest, aggregate wattage ratings like those quoted by the video card makers are complex beasts, and not directly comparable between supplies.
Then there are those that go the other way. Dell consistently stamps their supplies with very conservative ratings- frequently 50 W or more below the supply's real capabilities. PC Power & Cooling rates at more realistic temperatures than many others, and the difference can be enormous.
So really, the question is less about quantity and more about quality. The plain fact is that a well-made 350 W power supply is likely to handle just about any average computer with any mainstream video card. A well-made 450 W supply is all but guaranteed.
This of course neglects dual-video-card setups like ATI's Crossfire and nVidia's SLI. 2 cards use more power than one (fancy that). "SLI certified" supplies are very much available, and if you want a promise it'll work they are a good route to go. The supplies that carry that sticker are generally very solid and very capable. But again, a well-made 450 W supply can handle many not-ridiculous dual-card configurations. Well-made, high-rated (550 W or so) supplies that don't have the magical certification from nVidia are often quite competent to deal with very demanding dual-card systems.
The short answer to the title is thus: If it's a quality power supply, then very often yes.