There are really two different types of food delivery in this thread grocery delivery (to stock your kitchen) and restaurant meal delivery.
I'll leave it to others to discuss restaurants that deliver hot meals.
There are three WDW-area grocery delivery services. At a high level, each of these services is similar. You tell them what you want delivered, and they deliver the items to your resort (either to your room/villa or to bell services). You pay a premium over the actual grocery prices to account for picking and delivering the items.
WeGoShop
http://www.wegoshop.com/
WeGoShop is the only service that I've used. I like their concept the best. You submit a freeform grocery list. You can be general or specific ("carton of orange juice" or "64 oz Tropicana Pure Premium Orange Juice with No Pulp"). You can specify which grocery store you prefer, such as Publix, Winn-Dixie, or
WalMart. You pay the cash register receipt price plus a reasonable shopping/delivery charge. You must reserve a delivery date and time in advance, which allows the owner to stay on schedule with deliveries. If you search for "wegoshop" on DIS Boards, you'll find many good reviews, but also a few bad reviews from 2005. The Central Florida WeGoShop operation changed hands on late 2005, so you should be able to ignore any bad reviews from 2005.
Goodings
http://www.goodings.com/ (click on "Online Shopping")
Goodings is a small, terribly overpriced grocery chain in the WDW area. They have a nice, web-based shopping service. According to their site, "a $50.00 minimum order is required and a $20.00 service charge will be added to your total." Given their high prices and the service charge, my guess is that they'll generally be more expensive (possibly much more expensive) than WeGoShop. However, people on this board have posted good reviews. My understanding is that they generally deliver to bell services.
GardenGrocer
http://www.gardengrocer.com/
GardenGrocer has an attractive website. You can pick and choose grocery items from GardenGrocer's sophisticated website. There have been many favorable reviews of GardenGrocer, but recently there was a thread called, "
TERRIBLE Experience with Garden Grocer." This thread includes both sides of the story. The owner of GardenGrocer tried to defend himself. However, it seems he really dropped the ball and subsequently failed to take the initiative to make things right with the OP. GardenGrocer might be a victim of their own success. Some posts later in the thread suggest that the owner of GardenGrocer learned from the experience.