I don't have a car in Tucson but my house has one. You can shop for groceries and get around town easy enough on a bike (and it is a great biking city!) but for purchasing things while moving in (you try biking pillows and laundry detergent around town!) and for buying more than a six-pack of beer, a car helps. The nice thing about Tucson is that you can live within walking/biking distance of the university and a supermarket and the downtown bar area VERY CHEAPLY. That said, many people I know who came without cars ended up buying one. It depends on how dependent you are on cars (I'm 24 and never owned one) and what your living situation is like (ie: can you borrow one to make major shopping trips). Also, if you like to hike/camp/get out in the wilderness, it's nice to have a car on hand. But that's true even in cities with great public transportation.
My advice, come without one, buy one here if you feel the need...