Perennial weeds are not a problem on our farm. I have had success no tilling tomatoes, pumpkins, sweet corn and peppers, as well as fall broccoli. Pumpkins, in particular, are a lot cleaner, because the soil doesn't splash up on them when it rains. The University of Maryland is doing all its pumpkin research using the no-till method. Eggplant, melons and even snap beans can even be no-tilled.
Some organic farmers are no-tilling tomatoes and pumpkins.
In 1997 I left 1 acre of pumpkins unsprayed with herbicides and had excellent results. The cover crop of hairy vetch kept weeds from growing. Then this past year I did the same test and got unsatisfactory weed control. The problem was that the cover crop was not thick enough. I think no-tilling can be done organically on a small scale with a good cover crop and for later planted vegetables.