I'm assuming your apartment has windows (or do you live in the dark?) so invest in some window boxes. You can grow herbs easily in those.
I was hoping there was some secret vegetables/herbs that could deal with low-light. I guess that means things that would be possible to grow in the woods, like underbrush.
I did make a great discovery this year: chocolate mint (mentha piperita). The leaves taste like minty chocolate (you really have to try this -- you won't believe it until you do).
Also, I've heard conflicting reports about growing mint indoors over the winter; some sources say that mint needs to die down in the winter and won't survive year-round growing, but others don't mention it. Should I just plant two pots, one indoors and one out?