Potatoes are the foremost item grown this way. Growing potatoes from seed is generally a crap shoot. But when you use a tuber, the resulting plant is like the mother plant. I grow a number of potato varieties. My favorites are La Ratte, Purple Majesty, Red Thumb, Elba, Dark Red Norland, Carola, and a pink fingerling from Peru that I don't know the name of. There are others, but this year this is what is going into the garden.
Other veggies propagated vegetatively include....
... Sweet Potato
... Okinawan Spinach
... Cholesterol Spinach
I've also done vegetative propagation on leeks, onions, chives, Holy Basil, rosemary, stick oregano, kale, collards, a cauliflower called Violet Queen, and tomatoes. Of these, I still do tomatoes and stick oregano.
Pineapples, strawberries, sugar cane, and bananas are also reproduced by this method,
I could try others but I haven't experimented beyond these yet. Just give me time!