We also just get about 6 hours of sun. Last year was my first garden at this house. I did tomatoes, peppers, onions, greens, herbs, beans, cukes...
The cukes were low producing, and the pepper plants never even got to full size -- and only one made even an attempt at making a little fruit. But, we had a TERRIBLE summer. The 6 hours of non-shade didn't translate into 6 hours of sun, when it rained like 2/3 of the time. And it was quite cool. So, no peppers.
Everything else actually did quite well. Greens were fabulous. Herbs were huge! Onions were fine. Even the tomatoes did fine -- I had problems with septoria and blight, but that's because of the weather, not the shade. The plants grew enormous, and set TONS of fruits which grew very well.
I didn't get a full harvest only because I'd planted late, screwed up hardening off, and almost killed them. They were probably about a month 'behind' by the time they actually started growing properly (at which point they TOOK OFF!) So I harvested about 50lbs of green tomatoes, to ripen indoors.
I have no doubt that if we'd had a more normal summer, and I'd got them out at the right time (and without nearly killing them in the process), I would have had a bumper crop of vine-ripened tomatoes. Even though they only get 6 hours of sun, and were on the north side of the garden to boot!