Most gardeners know that you can save the seeds from many vegetables to plant the following year.
Many also know you can buy things like horseradish and ginger at the grocery store to plant.
Did you know that you can buy a celery stalk, cut off all but the bottom end, and replant it? Sure enough a little celery plant will spring up from the center.
Likewise you can replant the bottom portion of onions, both large and scallion. As long as you have the root end, the plants will regrow.
We also keep our smallest onions to replant the following year, giving them another chance to get bigger. It's also because nobody wants to peel the smaller ones.
Potatoes that are leftover from the previous harvest, or store bought ones that have started to sprout, can be replanted. If need be, they can even be started indoors, giving you a bit of a jump on the season.
Sweet potatoes are a crop you should only ever buy slips for once. Save some of your harvest to grow over the winter indoors, and replant when the weather is warm.
Of course you will want to get them into the ground as soon as possible when the weather is right. For potatoes and onions, that's early in the spring; about 10 weeks before your last frost. Sweet potatoes and celery prefer the warmer temperatures.
You can try this with store bought herbs as well, if they still have the roots intact. Often though these are grown hydroponically and don't adapt easily to transplanting.