The food here is generally quite good; I recommend getting the falafel king combo ($9 for a ton of food). I emailed Falafel King to find out which items are vegan and here is their response as of 12/30/12:
Falafel, Hummus, Tahini, Baba Ghanoush, and the Pita are all vegan. The rice is also vegan, the red flakes you see are shredded carrots which give a unique touch. The grape leaves are vegan prepared with rice, diced tomato, diced onion, and seasonings. The hot sauce is vegan with no dairy or animal products. As for the spinach pie, this menu item contains feta cheese along with the spinach and diced onions.