I must have bad luck with graphics cards. My last graphics card was an XFX nVidia 8600GT. My current graphics card is an EVGA nVidia 9800GT. Both have failed in unexpected ways. Fortunately, I have been able to fix both of them! WARNING - these procedures will most like void the warranty, if you have one.
XFX 8600GT
Exploding Caps
One evening I was sitting watching TV in another room with my wife. We heard some 'pop' noises. Well, more like several loud 'cracks'. My wife asked me what the sound was. I thought it was the ice maker in our fridge. Suspiciously, though, the graphics on my computer started having problems. I began seeing artifacts here and there. Then, more pops and the display become incredibly garbled and unusable. I pulled out the graphics card and what you see above is what faced me. Numerous aluminum electrolytic capacitors had exploded. You can see the paper separator(the yellow fibrous stuff) spewing out.
The Fix
To fix the 8600, I purchased some aluminum electrolytic capacitors from Digikey with the same values as the exploded ones. Generally, caps that large have their values and ratings printed on them. I needed some 1500uF 6.3V, 1000uF 6.3V, and 470uF 16V capacitors. The footprints for the capacitors were generic and supported multiple sizes, so I just got the cheapest ones in approximately the same size. Radial capacitors have 3 dimensions to consider. Lead spacing, diameter, and height. In retrospect, the replacement 1500uF caps are a lot taller than the original, but they still fit in my case. I wouldn't worry about stressing too much about matching ESR or any other features other than capacitance and voltage rating. Odds are that the originals are on the cheaper side.