I believe some of the restaurants at Downtown Disney won't take them, but most places (even the little stands) will take gift cards as payment for food. On my last trip, I didn't want to carry cash with me so I only used a (well-stocked) gift card
We used a gift card for our gratutities, souvineers, etc last week without a problem. We ate at Raglan Road, Yak & Yeti, Flying Fish, Beaches & Cream, Biergarten, Cape May, Whispering Canyon, 'Ohana, and Via Napoli. We bought stuff at the DTD Disney store, Mouse Gears, and the tea shop in the UK. We also bought my husband a 9 day park ticket at the booth as you go in the back entrance to Epcot. No one thought twice about accepting the gift cards.
Last Oct I used a left over one day park ticket, an old gift card that still had about $125.00 left on it, and a Disney Rewards card to buy my AP. I round up paying .71 cash for my current AP. lol