Maybe something tropical, otherwise probably need to put plants right under lights/next to south window. Windowsill herb gardens have been done for years, so there might be some scope for small, compact vegetables tolerant of (modified) indoor conditions.

Mesclun should do very well. Any kind of greens. But the other things are going to require more sun than you have.
You can start off planting a mesclun mix or other baby greens in a flower pot. You should be able to get a crop inside of a month! And it's cut and come again. The English grow their mustard greens in a saucer - you can sprinkle the seeds on a paper towel and they will come up fine as long as you keep it moist. And you can sprout all kinds of seeds (mustard, cress, alfalfa) in the same way or in pot filled with potting mix. No extra light required.

tomatoes work.

Here are some good options for you check them out

Here is a link that might be useful: Indoor Vertical Gardens

Check this out
http://www.npr.org/templates/story/story.php?storyId=125504307

That link above me is a total scam, I clicked on the link by growgoods above that and somehow that comment appeared when I closed it.