Many varieties of strawberries grow wonderfully in containers, including barrels, drums, or bags. Many seed companies and garden centers offer pouches or bags, complete with plants, for growing them vertically on walls and fences.
Personally, I like them in hanging baskets. With their green leaves, red fruit, and delicate white flowers, they're actually quite pretty. And when the juicy red fruits cascade down the sides of the basket, they are practically screaming for you to come over the pick them.
Like the growing bags, baskets save on patio space and keep the fruit up off the ground and away from mold, insects, and birds (mostly). Another idea is to grow them in planter boxes attached to railings or under sunny windows.
When planting in containers: