tokala
Emperor
I have 2 PCI-Express slots--a x16 that houses the current video card and a free x1 slot. I gather the new card will have to replace the current one in that slot. Not sure if it's PCI 2.0, though--my manual doesn't specify, so I'm worried that it's not (the system is a Dell Dimension 9200C, in case you're wondering).
My thanks to you, Quintillus, and tokala for your help.
If you have a Dell, chances are that that you have non standard form factor power supply with a rather limited power output. In that case a card as powerful as the GTX 460 might give you trouble or even won't work at all, and it will not be possible to upgrade the PSU
Ballpark figures for the typical gaming power demands of some video cards
HD 4670: 50 W
HD 5570: 30 W
9800 GT: 75 W
HD 5750: 65 W
GTX 460: 120 W
Worst case can be ~30% higher than that. You should check out the specs of your power supply. For the GTX you will need at the very least 300 W with a high current capacity on the 12 V rail. The most powerful card that will work in probaly all reasonably modern computers would be the HD 5750. The HD 5570 should work in anything that has an PCIe slot
Edit: All different PCIe Standards are mutually compatible. The worst that could happen would be a very small performance penalty. No fried computers anymore like good old AGP.
Edit 2: Is the Dimension 9200C a small form factor case? Than you will need a single slot, low profile card. The more powerful cards are usually not available as low profile.