M is also worth seeing. I suppose it was the first serial killer movie, as well as Peter Lorre's screen debut. It's different from modern movies insofar as the serial killer is rather pathetic. But the film itself is haunting and is drenched in that marvelous 1920s German expressionist look and feel.

Edit: not Lorre's screen debut, but his second appearance, as I just found out from this superb piece: http://www.logosjournal.com/issue_4.4/leming_printable.htm.