We just returned from WDW earlier this month, and we visited in January and March of 2013. I know things change, but here are our experiences (I am gluten-free and vegan (no animal products or meat), and DD is allergic to tree nuts, coconut, and shellfish).
Ohana at the Polynesian was able to accommodate us for breakfast and dinner. We had to wait a very long time for our food (even though our needs were marked on our reservation) and it was WAY too much food, but it was really good and plentiful. They customized our whole meal, and it was fantastic. I posted photos a long time ago in the vegan and vegetarian thread in the Dining forum (you might check there, as a lot of us are vegan and we share our experiences in dairy-free and egg-
free dining). We had bread, appetizers, I had a huge salad, a giant, gorgeous, delicious stir fry, and a sundae with DF ice cream and Enjoy Life cookies and chocolate sauce. My kids still talk about that sundae and how good it was (I had to share because I could really only take one bite- I was SO FULL!!!).
Kouzzina on the Boardwalk was fantastic, too. They understand allergies, and they take very good care of you. No one will leave hungry.
Babycakes NYC (in Downtown Disney) has vegan and gluten-free cookies, doughnuts, and cupcakes. The cupcake frosting is gross, but the baked goodies are great! They also have small servings of Babycakes in some resort food courts and in the allergy stand at Animal Kingdom.
Teppan Edo in Epcot is great. They will prepare your meal first, on a clean grill, or in the back on a separate pan.
Cosmic Ray's in MK is one of the only counter service places where I have had a good experience. They have GF/EF buns, a GF fryer, and will use a green tray to signify a food allergy so no one "accidentally" dumps cheese all over your dairy free food like they did at the Mexican counter service in Epcot.
You can look at the menus on Allears to scope out possible food choices before you travel, but remember you will still have to ask questions once you arrive.
And do check out the vegetarian/vegan discussion in the Dining forum. We have a lot of people avoiding egg, shellfish, gluten, dairy... many with allergies too. It is a great source of info!