I am on Win 7 using an Nvidia GT240 graphics card. I am only given an option for 640X480 in the video options tab of the settings. The problem is that the left and right edges of the screen (I'm guessing about 50-70 pixels on each side) are cut off. I also don't seem to find any registry setting that will permit changing to 1024X768.

Any ideas?

Well one solution is that you can download the Freespace Open Engine and get resolutions much better than 1024x768. :) The modern open source engine really does make the game look nice and improves compatibility/fixes bugs. So I'd recommend it.

However, if you want the classic FS2 graphics, I'm afraid I can't help you with getting those working though there are a few here who can. If not, you can try the hard-light.net forums (they will also recommend the FSO engine, but are often knowledgeable about vanilla FS2 as well).