What should I NOT state in a cover letter?

First and foremost, you do not need to restate your entire resume.  Anybody reading your cover letter will also have your resume.  Second, you do not need to kiss the ass of the reader by saying things like “I know that bank XYZ has the smartest people, most dealflow and is the coolest place to work!”  If you have a concrete reason why you want to work at that bank then yes, say so (in ONE sentence) but if you go too far, you come off sounding naive.  After all, for the most part banks (at least bulge brackets) are pretty much the same.

Third, don’t go overboard stating how great you are.  Just about everyone applying to investment banking is “smart,” “hardworking,” “enthusiastic,” etc.  The reader will judge these traits by your resume (where you went to school, degrees, GPAs, test scores, prior work experience/internships, etc.). Finally, don’t say how the firm is going to benefit by letting you work there.  To them, you are just one more potential Analyst or Associate.  That is to say, you are a commodity.  No Analyst or Associate that is new to banking is going to be able to contribute significantly for months, so to state otherwise makes you once again seem naive.