Aircraft mechanic here. How stripped out are the screws? How did they get stripped out? If there is still some edge left, you can get them out just by pushing down VERY hard as you try to turn them. At work we'd use a speed handle, which looks like this:
It allows you to put your entire body weight on the screw if necessary. (Though I wouldn't use that much force on a graphics card!) This is the quickest, safest, and most desirable solution. You probably don't have a speed handle, but a manual screwdriver is preferable to a power drill as you have more control. You'd obviously need to secure the card in a way that you don't damage it.
With the screw extractor, again the key is to push down HARD. The teeth have to bite metal, and that takes force.
If that doesn't work, just drill it out. Serously though, this solution sucks- you stand a good chance of messing up the threads on the card, and may cause even more damage than that if you miss. Clamp the card so it doesn't move, use a bit smaller than the screw diameter (but only barely), be very careful to drill straight down, and don't go deeper than the screw. This is the most dangerous solution; try everything else first.
Anyway let this be a lesson; don't frigging strip out screws. When your screwdriver is turning and the screw isn't, even a quarter turn, you need to push down harder.
Edit: It's also important to make sure that the screwdriver fits the screw. Otherwise you have worse grip, and are more likely to strip it out. Same goes for the extractor.
Another edit: In the future, don't overtighten screws either and you won't have this problem. Especially in no-vibration, low stress applications (like pretty much everything in a computer), snug is fine. Don't crank it down as tight as you can! They aren't going to spontaneously unscrew and fall out.Edited by Traches - 5/24/11 at 10:06pm