Le Dog is probably the only hot dog stand in America where you can get your red hot with a bowl of lobster bisque, posole, or any number of excellent soups which change daily at the whim of management.  Two locations, on Liberty, and on Main street; it's been written up in foodie magazines for the great quality/value combination.  Pretty much a lunch-only option, although they are occaisionally open at night at the Main street location.

Olga's Kitchen in the Briarwood Mall:   They do mainly gyro sandwiches with a bent on the bread - they use a secret recipe to make a to-die-for bread. The restaurant is always busy, but you rarely wait very long to be seated.  They have servers and it feels like a diner.  The food is reasonably priced and always hot.  Olga's can only be found mostly in Michigan - the good part is that they have coupons all the time (holiday's are triple coupon days).  

Pizza Bob's is a good choice for those looking for a milkshake.  They have a variety of flavors, like caramel and chocolate chip, that you can mix and match. The chocolate they use for the chocolate chip is more like the stuff that hardens when you drizzle it over ice cream - so you end up with a shake infested with more chocolate chips than you can imagine. 

Truly original in Ann Arbor includes the pervasive Chipati (sort of a salad sandwich wrap) and the one-of-kind Garden Pizza you'll find at CUBS' A.C.

Try the breadsticks and cinnamon breadsticks at Pizza House.  Not quite baked all the way through, but still baked enough that you're not just eating dough.