pretty much every table service restaurant has some vegetarian option at disney.
check out the menus section of allears.net for full menus and prices.
for quick service,
In EPCOT, Japan has sushi as quick service, morocco has a lot of options at the quick service such as tabouleh and hummus.
Veggie burgers are available everywhere.
Sunshine seasons in the land pavilion has veggie stir fry and soups.
Fish and chips at UK.
beans and rice in Mexico.
In AK, Restaurantosaurus has a grilled veggie sandwich with sweet potato fries.
There are salad and fresh veggie snacks and fresh fruit available at a lot of places all over the parks.
Plus pastries, ice cream, soft pretzels (the ones in sommerfest in germany are amazing), popcorn, funnel cakes, crepes.