I really enjoy the vegetarian combination plate at San Angel Inn, and if you enjoy Mexican food, you might as well. You have to specifically ask for a vegetarian menu when you get there - the vegetarian meals are not on the regular menu.
If you want some place that has more than just one or two veggie options, I think certain buffets are the way to go. Boma definitely has quite a few options on their buffet, and at least the last time I ate there, Crystal Palace also had a decent selection of veggie options on their buffet.
I haven't eaten in Italy in quite awhile, but I don't recall it being very veggie-friendly at the time (then again, this was before it changed hands...maybe now it's better). I do like Mama Melrose in DHS - very tasty flatbread pizza. Not sure what else they have that's veggie though.
Every Disney-run table service will have at least one veggie option, and whether you like it or not will determine whether you think it's a good place to eat or not.
For nice lunch sandwiches, I like the Wave at the Contemporary, the Plaza restaurant at MK and Columbia Harbour House at MK (they also have veggie chili if you like that). But, each of these places have *one* vegetarian sandwich option, so if you don't like them, then...you probably won't like the restaurant.
