Lots of bulb-type plants grow corms. The one that I get the most use out of is elephant garlic. The corms take a couple/few years to make a full elephant bulb, but you will get an edible "round" after one year in the ground. I harvest the elephant garlic (not a true garlic) in the summer and replant corms in the fall after an hour soak in water.

Walking onions have bulbils at the top of the stems and propagate like mad.

Hardneck variety garlics grow bulbils that can be replanted as well. Of course I always miss a head or two and the whole garlic sprouts in the bed.

Archaeologists think that wheat varieties that we cultivate may have been selected for by how easily the seed is removed from the plant during transport home (accidentally, not on purpose). Similar effect I suppose.

John Scheepers has several varieties:

http://www.johnscheepers.com/catview.cgi?_fn=Product&_category=Best:Brodiaea

Sue

Potatoes will often "reseed" themselves when small tubers are left in the ground after harvesting the large ones. Even here in the rainy northwest, they seem to grow without rotting... at least in raised beds.

Sue

garlic, tomatoes root almost overnight if you are interested in cloning, all they need is water in a glass most of the time

Jeruserlem artichokes will nearly always regrow from bits of left behind tubers