Redd Rocket's Pizza Port in Tomorrowland has several salads without meat, spaghetti w/Marinara sauce, and a vegetarian pizza.
The French Market in New Orleans Square has a baked pasta gratinee that is wonderful.
I think Cafe Orleans (also in NOS) has Ratatouille.
The Big Thunder Ranch Barbecue has a vegetarian vegetable skewer (has tofu, onion, I think bell pepper and some other stuff) which is very tasty, and the sides are all vegetarian (barbecue beans, cole slaw, corn bread, and corn wheels at dinner).