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he is hilarious in roles in which he isn't meaning to be funny.
I agree. I love Midnight Run, where De Niro was part of an excellent ensemble of actors. This movie had some hilarious moments, but it wasn't a "comedy." The same goes for King of Comedy. (Can you imagine Scorcese directing an out-and-out comedy movie?)

Analyze This and Meet the Parents were clearly situation comedies. De Niro was playing off comedy actors. It would be interesting to see him paired with Robin Williams.