Carrots, lettuce, onions and beets come to mind, although with every crop, the trick is in finding the right variety for every season. The summer can be an obstacle for lettuce while you can also choose between green and bulb onions.
Tomatoes can't survive the cold winters, but if you have a greenhouse, you can grow them year-round. You could also put them into pots and bring them inside for the winter. You can do the same with peppers to get them to grow year-round.
A lot of it probably depends on your planting zone. You could probably grow a crop of trees through the winter, as long as they aren't evergreens, just about anywhere in the U.S. where the ground doesn't freeze for long.