I'm not sure where I picked up this gem:

Various plants (in no particular order) that you can regrow from the food you already have! Way to reuse and recycle!  

Apples- http://www.ehow.com/how_2135774_grow-apple-seeds.html

Tomatoes- http://www.ehow.com/how_5581958_grow-tomatoes-fresh-tomato-seeds.html

Potatoes/Sweet Potatoes- http://www.gardenguides.com/117543-plant-cuttings-potatoes.html

Green Onions- http://www.17apart.com/2012/02/how-to-grow-green-onions-indefinitely.html
http://tipnut.com/nifty-food-plants/

Leeks- same technique as green onions

Carrot Tops- http://www.gardeningknowhow.com/children-in-the-garden/grow-carrot-tops.htm

Pineapple- http://www.rickswoodshopcreations.com/Pineapple/pineapple.htm - I've got a couple of these going!

Romaine Lettuce- Same technique as celery

Cabbage- Same technique as celery

Celery- http://www.17apart.com/2012/02/growing-celery-indoors-never-buy-celery.html  - wish I'd remember about this one!

Avocado -http://www.thehungrymouse.com/2009/09/09/how-to-grow-an-avocado-tree-from-an-avocado-pit/ - I have a horrid time trying to get these to start.  If someone has suggestions (or a sapling!) I'll take it!

Lentils- http://foodstoragemadeeasy.net/2009/02/19/how-to-grow-sprouts/

Pumpkin- http://pinterest.com/pin/98375573080950437/

Ginger- http://www.gardenswag.com/2011/12/5-foods-you-can-grow-from-kitchen-scraps/ - I'm actually growing one of these!

Garlic- http://www.gardenswag.com/2011/12/5-foods-you-can-grow-from-kitchen-scraps/

Bonus: Bok Choy - http://www.17apart.com/2012/02/how-to-regrowing-bok-choy.html