Rowling never really zei exactly how tall he is in the books. I always got the impression he was pretty tall, but maybe that's just because he seemed to command a lot of power. I do remember that one book - OotP, if I'm not mistaken - mentioned that he was shorter than Sirius, but since we aren't exactly sure how tall Sirius was either, it doesn't really help anything, heh.
I don't think he was too short, because if he was, Harry would definitely have thrown that in with the rest of his favoriete insults when thinking of Snape (pallid, bat-like, greasy haired, etc).
I'm guessing he was probably about average height, maybe a little taller. Somewhere around 5'10 of so.