In the original I don't recall him doing this too much. Maybe I'm remembering wrong.
Like Froman said, it was there in the first movie, but it just kept growing film to film, almost to the point of turning Freddy into a caricature of himself by the end of the original run. Wes reigned it in with New Nightmare, but the schitck returned to near slapstick levels in Freddy v. Jason.
Either way, it was non-existent in the remake, if I remembering right, which misses a huge part of the spirit of the franchise.