I know that Visa, MC, Discover, & AE are accepted at all sit down restaurants and all the gift shops. I think the same cards are accepted at counter service food locations. I saw a post that said a lot of the carts were also accepting cards with more carts being added as time goes by.
So the answer is [or soon will be] that all major cards [including bank check cards with Visa or MC logos] are accepted everywhere at WDW.
There are also ATMs at all the resorts and in all the parks. There is a $2.50 fee to use the ATMs plus whatever your bank may charge.