The seared maize cake with hot pepper sauce at Jiko was so good that my DH called the manager over to thank Jiko for taking vegetarian dining seriously (it was new the week we were there, the week of September 7 ... it was a re-working of the maize-stuffed hot pepper they used to have and it's not listed on AllEars or WDWInfo yet, but it is on the official WDW site). He also really liked the mango-glazed tofu at Sci-Fi. At Mama Melrose I had the tomatoes and mozzarella appetizer (wonderful, good quality and fresh) and the penne a la vodka without the pancetta, and it was definitely the best penne and vodka sauce I'd ever had. They do have other options (DH had the tomato and spinach flatbread and there's an eggplant thing too). We had breakfast at both Boma and Cape May and thought they were both outstanding ... the tomato onion African curry and the not-sweet cinnamon rolls at Boma and the cheese omelet and asparagus at Cape May were the standouts, but everything we had was very good.
For quick service, Wolfgang Puck Express had a couple great sandwich options. Columbia Harbour House has a hummus sandwich and veggie chili. Picnic in the Park at Animal Kingdom had a so-so wrap, but the tandoori tofu side was absolutely wonderful. We ended up eating more veggie burgers than we would have liked (3 in 10 days), but that was lack of planning on our part—if we'd planned better we would have not waited until we were starving and had to eat the nearest available thing. He had a tofu and veggies noodle bowl at Sunshine Seasons in Epcot. I've also heard Morocco is really good but we didn't make it (see above re: not planning well enough).
We do eat seafood so only maybe 1/3 to 1/2 of our meals were actually vegetarian, but those are the vegetarian ones that really stood out. We're also not as detail-oriented as most, so for example he didn't ask what was in the broth in his tofu veggie noodle bowl and I can't swear to you it was truly vegetarian.