An idea for those who want fresh produce without digging a garden bed, especially if you have lots of leaves or hay to put to use. This also can get very high production for the space needed.
Grow potatoes in a barrel or (clean) garbage can. I haven't done this myself, but I have known people who did. Put a few inches of soil and compost at the bottom of a barrel with a few drainage holes. Put in 3 or 4 seed potatoes (get real seed potatoes; this won't work with potatoes from the store which are treated to discourage sprouting). Cover them with several inches of hay, straw, or leaves (mix leaves with compost, sawdust, hay, or straw) and water well. Water every two or three days (enough to wet things down without waterlogging it). When shoots start pushing up through the mulch, add several more inches and wet it down. Keep repeating this. When the plants get close to the top of the barrel, just make sure it gets water. After 3 to 4 months when the leaves start turning yellow, "harvest" by dumping the barrel over and shaking the mulch away from the potatoes. It can be a good idea to do this near a compost pile or garden bed because the "bedding" material from around the potatoes can be added to the compost or used as mulch now. I've heard of people getting 50 pounds or more of potatoes from a single barrel, but I don't know if that's exaggerated or not.
Just to repeat one warning: don't try to use potatoes from the store even if they sprout (unless you've bought them from a really good organic store). Even if they sprout, they rarely survive. At least the first year, buy real seed potatoes (and learn how to store properly if you want to save your own seed potatoes). Cut them into pieces with at least two eyes per piece and allow to dry for a day or two before you plant them. And while you want them to stay moist, potato plants will rot if they get too much water. This is a good opportunity to try some of the non-Irish potato varieties that tend to be pricey if they're even in the store.
The plant needs some sun once it's over the top of the barrel, but keep in mind you don't want the potatoes to cook in the barrel either if you live in a hot climate. Warm climate gardening can call for planting at different times of the year from other areas, and you may also want to place the barrel to get shade during the afternoon or partial shade most of the day.