Every trip I have ever taken to WDW has been as a vegetarian. I have never once gone hungry.

Actually, I have great luck in finding wonderful food all over the "world."
I'm not sure if you are looking for more help for CS or TS or both, so I'll try to be as helpful as possible and give you an idea of what to expect and what I have experienced myself.
CS -
MK:
Cosmic Ray's - This is my favorite CS in MK. I read that a PP had problems there, but I never have. Actually, my family tends to eat here at least once, but usually twice each trip. One staple that you will generally find at most CS is the veggie burger, unfortunately Disney has changed their veggie burger and while I personally do not care for them, many do. I will still eat them, but I tend to hit the toppings bar pretty liberally. I also like the veggie wrap that they serve here. Be aware if you have no been to Cosmic Ray's it is broken up into bays. One section for burgers, sandwiches/wraps and chicken/ribs. Veggie burger is of course at the burger bay while the veggie wrap is at the sandwich/wrap bay.
Village Haus - Not a bad place if you are looking for a personal cheese pizza. They used to serve a veggie pizza that I really liked, but I haven't seen it on the menu lately. They also serve a Mediterranean salad that can be served without the chicken.
Pecos Bill's - Veggie burgers are the vegetarian go-to meal here. You can ask that the taco salad be served without meat, though. A few years ago they had a great salad that I ordered without the chicken, but it looks like the taco salad replaced that one. Outside of this restaurant is supposed to be a cart that sells veggie flatbread, but I haven't tried it yet.
Tortuga Tavern - Was once El Pirata y el Perico. This is one I will probably try in September as they are supposed to serve veggie tacos.
Columbia Harbor House - This is where a lot of vegetarians love to eat. The restaurant offers a Lighthouse Sandwich - hummus with tomato & broccoli slaw. I wanted to love this, I really did. I love hummus, thought this would be excellent. Unfortunately, my sandwich had a TON of slaw on it and I couldn't taste anything but the slaw. I don't know if it was the fact that there was so much slaw or the combination of the two, but I didn't love it. I was planning on trying their veggie chili, but I just read that it has been taken off the menu. They also serve a salad that can ordered without the chicken.
Main Street Bakery - I gotta be honest, we go here for the cinnamon rolls. BUT! They have a sandwich that I have been wanting to try, it sounds great! Tomato, buffalo mozzarella sandwich with basil. Yum! Sounds like a caprese sandwich to me! I love those.
Epcot:
Sunshine Seasons - My favorite place to eat in Epcot for CS. There are quite a few options here, but my favorite is the tofu noodle bowl. Yum! It was SO good. I wanted to kick myself last year on our second visit to Sunshine Seasons. I made the mistake of ordering the veggie sandwich after trying that tofu noodle bowl a few days earlier.. Bad move on my part. I was wishing I ordered that tofu noodle bowl a few bites into my sandwich, it was that good to me. They also serve veggie sushi and the desserts are amazing!
Tanigerine Cafe - We eat a lot of hummus at home and I was looking forward to trying their vegetarian platter since hummus is listed as one of the items. I don't know if it was a off day for the restaurant or not, but this is one of the only places we won't be going back to. It was just that our food wasn't good (my husband had the meatballs and didn't care for them either) but the service left much to be desired. Now I will stop in here for a cup of coffee and a piece of baklava, but we won't stop here for a meal.
Liberty Inn - Veggie burgers are offered here. They used to have a veggie wrap, but when we were at WDW last February it was removed from the menu.
I sometimes have a hard time finding good CS other than at Sunshine Seasons when it comes to Epcot. I will let you know that Lotus Blossom Cafe used to use chicken broth in their food preparations, whether or not this is still the case, I'm not sure. The Yakitori House has sides of rice and a house salad, but nothing in the form of an actual vegetarian menu item. Kringla Bakeri og Cafe in Norway has a potato, goat cheese and vegetable torte - I haven't tried this, not a fan of goat cheese. They also serve fruit cups. La Cantina de San Angel sells cheese empanadas and I've read that you can get a cheese quesadilla.
AK:
Flame Tree BBQ - I loved my fruit plate. It was very filling and refreshing. I will tell you there is no indoor seating here and the birds can get a little aggressive.
Pizzafari - Cheese pizza and bread sticks.
Restaurantosaurus - Veggie burgers can be found here. I have also read that you can get the Dig Site salad without the meat. I had a veggie burger here last February and noticed they have a decent toppings bar. Not as good as Cosmic Ray's but not bad! And they added a new menu item since we were last there: Vegetable Subosaurus - grilled vegetables, mushrooms, onions, provolone, served on a toasted roll with sweet potato fries. Sounds promising!
Yak and Yeti CS - Gotta be honest, I haven't tried this once since I couldn't see anything on the online menus that I could eat. Now that might not be the case, but that's what I've seen so far.
DHS:
I don't have any experience with this park.. We always skip it. Sorry!
Resorts:
AK/The Mara - Love this place! I had a very unusual veggie burger here a few years ago. It had traces of cumin taste and it was smoky and wonderful. I don't know if it is still on the menu as they can change often, but if it is still there I'd be happy to order it again. They also have a vegetable flatbread and a falafel pita. Yum!
Poly/Capt. Cook's - My favorite of the resort CS. Great cheese flatbread! Yummy adult grilled cheese sandwich, veggie sushi and stir-fry noodles that can be made without meat. Cannot wait to go back. You can also get Dole Whip here.
WL/Roaring Fork - The grilled vegetable sandwich is pretty good and there are a few salads as well. They also sell a cheese flatbread.
POR/Riverside Mill - Quite a few options like a pasta and pizza. We preferred breakfast here.
This year we will be trying GF/Gasparilla Grill and Games. They have a vegetarian lasagna and a tabbouleh pita. The vegetarian lasagna sounds good! I have also read good things about Contemporary/Contempo Cafe. The menu shows a veggie bake, pasta marinara and flatbread. Sounds good!
TS -
MK:
LTT- I love this place! Lunch is wonderful! The Colony Salad without the chicken was the best salad I had all week last year.

They also have a veggie pot pie for lunch. We also enjoy the dinner. While they usually bring out a vegetarian entree during the dinner, I love the salad, rolls, potatoes and veggies.
Crystal Palace - This restaurant is quite good. We prefer it for breakfast but there are plenty of vegetarian things on the buffet for lunch and dinner. I've also had a chef walk me around the buffet for both lunch and dinner. Very helpful!
Now we haven't tried Tony's, The Plaza or CRT yet. CRT is actually booked for our September trip. The vegetarian entree currently being offered is a vegetarian cassoulet. Tony's sounds like it has a few good vegetarian entrees like the eggplant and The Plaza offers a veggie sandwich, but like I said we haven't been there yet.
Epcot:
Coral Reef - Despite being a seafood place, I was pretty happy with my vegetarian entree. It was a few years ago and they no longer serve that particular meal but I have to tell you the newer item sounds better to me!Mushroom Phyllo Crisp - roasted mushrooms, wilted Arugula, aged cheeses, rustic tomato ragout.
Biergarten - LOVE this place! I have always found more than enough to eat here and the last time we were there a fantastic chef not only walked me around the buffet but also made me a few items. Just fantastic!
Garden Grill - Our favorite character meal. The food was wonderful! The vegetarian entree that was served last year is a little hard to describe but it was very good. But I honestly ate more of the salad and rolls than anything else. This was the first time I had brussel sprouts that I actually really liked! The food was very fresh and tasty!
Akershus - Been here twice.. Will probably try it for breakfast in a few years, but we could pass up this restaurant and wouldn't miss it at all. The best part of our two dinners was the cold bar and the dessert. The pasta dish I had just wasn't very good at all. I won't go into the rest.
Marrakesh - Very good! Loved my vegetable cous cous. There was something so homey and familiar about the way the vegetables were served. Almost stew like. It reminded me of the way my mom cooked veggie when I was a kid.
We tend to be creatures of habit so we have skipped a lot of the other TS in the World Showcases. I will say that the vegetarian's shepard's pie at Rose and Crown sounds very good to me. Also Chefs de France offers two vegetarian entrees like the gratin de macaroni - that sounds good! Tokyo Dining was originally on our list of restaurants to try this year, but we opted to go back to Biergarten since that's the restaurant my son wants to celebrate his birthday at. Lots of wonderful options to be had in the World Showcase as far as TS goes.
Resorts:
Poly/'Ohana - Love it! I have always had a fantastic meal at 'Ohana. Besides being able to share the rest of the sides with my family they bring out a veggie entree. Last year it was tofu, stirfried veggies over rice. Very tasty! Like I said you get to share the sides like the salad, veggies, noodles and bread. Plus the bread pudding is wonderful!
Kona - This is one of the restaurants we prefer for breakfast. The noodle dish witout meat that I had before was fine, but nothing great and nothing special. Love Kona for breakfast, though!
Spirit of Aloha - The luau! Wonderful experience. We'll probably be back there next year. We opted for CRT in its place this time round. The food was very similar to 'Ohana for me. Loved it!
WL/Whispering Canyon - This place is a lot of fun! We're heading back here in September. They have switched the vegetarian entree since the last time we were there and I'm hoping it is as good as it was last time.
GF/1900 Park Fare - Love it! We've been here for breakfast and dinner and we enjoy them both! The strawberry soup is fantastic! There is always so much to choose from at the buffet. I really enjoy the sweet potato/red bliss mashed potatoes! SO good!
BC/Cape May - Despite being a clam bake, the dinner was wondeful! I had quite a bit to choose from and it all tasted fresh. We're actually trying breakfast here this time round. I've read that it is very good and that they have a vegetarian fritta.
AK/Boma - YUM! Love, love this place. The only reason we are not heading back here for dinner this year is to try Sanaa. The soups at Boma are wonderful and the chefs will point out what is vegetarian. They have the best hummus here! I think there are four different ones to try. So good!
Contemporary/Chef Mickey's - Unfortunately, this place gets a bad rep but we like it. The parmesan mashed potatoes are so good! And the Mickey shaped cheese raviolis are just fun and tasty. I've always had a good meal and haven't had any problems at all.
DTD/Marketplace -
I won't go into to too much detail here.. But I will say that we love T-Rex. So good and REALLY plentiful! We've also had good luck at Rainforest Cafe. I'm hoping that we can try Raglan Road and Portobello in the near future. It's been a few years but WPE wasn't our favorite. I'm sure it's better now and many people rave about the food. EoS is another one that's on our to try list.
I hope this helps a little! Feel free to ask any questions. There are lots of helpful vegetarians and vegans out there to help you!
