Limited on space or don't want the hassle of having to dig potatoes to harvest? Try growing potatoes in containers. I've done that the past few years in my garden with great success.
Any sized container will work, but obviously the bigger it is, the more potatoes you can get. Whatever the size, the container should have adequate drainage. The container I used was a 14" by 14" square container and I just harvested a nice harvest of red potatoes a few weeks ago.
In early spring, start by adding a few inches of a light potting soil or potting mix to your containers and place several seed potatoes spaced around the bottom of the container. Each seed piece should have at least 3-4 nodes on it. I used a dozen or so seed pieces in my 14" container. Cover the seed potatoes with 4-6" of soil and water well.
Once the seed potatoes have started to sprout and the foliage is growing about the soil level, continue to add more soil, leaving just the tops of the leaves showing. Do this until the container is eventually filled all the way to the top.
In the late summer or fall, you'll know your potatoes are ready to harvest when the tops of the plants start to yellow and die.
The best thing about this type of system is the ease of harvest! Simply dump over the container, loosen the soil, and watch your potatoes just roll out.
Potato towers are also a popular option and it's a similar growing method. Use chicken wire or some other wire mesh to create a ring, plant your potatoes in the bottom and continue to add soil or straw as the foliage gets taller. Pull up the ring, loosen the soil, and watch the potatoes roll out. Kids love seeing this and searching for the potatoes!
Something to try next spring!