Falafal and Schwarma are the hamburgers and cheeseburgers of Israel. You can find them almost anywhere, for a variety of prices, and different toppings. Falafal is made of chick pea and ground up with bread filling and either fried or baked. Its an excellent vegetarian option as it contains no meat. The typical falafal or schwarma sandwich is wrapped in pita with salad (tomatoes and cucumbers) in it, and drizzled with hummus. I've also seen it with baba ganoush (eggplant dip), french fries, tomato and avacado salad, sweet peppers and all sorts of other toppings. A challange is to find the best price. Mine was 3 shekel (around 75 cents) and I didn't think that that was too bad.
Schwarma is made from lamb meat (although it is frequently turkey) and cooked on a spit (similar to giro meat. Both are excellent choices and you have to have them at least once or twice in your stay. The best that I ever had was in the Jewish Quarter of the Old City near the arch.