YES! Many places have veg options. I've been two times since being veg, and I've found plenty. (Both DDs are veg, too, but DH is not.)
A few of my favs...
Columbia Harbor House in MK has a veg sandwich called Lighthouse. (There is also a veg chili that DH liked, but I've never been a chili fan.)
The counter service restaurant in Morocco in Epcot has some good veg options.
Sunshine Seasons counter service in The Land at Epcot has many veg options.
Although there was only one veg option each time that we visited Le Cellier (Canada in Epcot), both choices were fabulous (and Le Cellier is a steakhouse). Both times, I had questions about the choices and the wait person brought out a chef who talked to me and was very accommodating!
Crystal Palace at MK (Pooh and friends character meal) had many veg options at dinner.
On the other end, Akershus in Norway at Epcot and Garden Grill in The Land at Epcot were both disappointing veg-wise (Garden Grill was disappointing service-wise, too).
Check allears.net for menus to see choices.
http://www.allears.net/menu/menus.htm
And here is a good veg dining review...
http://www.disboards.com/showthread.php?t=1662538
Enjoy!