The single funniest moment from any of his films...
...is when he gets his face lit on fire by Juliette Lewis in Cape Fear and he's screaming and wailing and flailing his arms about before running out of the boat and jumping in the water. De Niro, as Max Cady, spends the whole movie demonstrating his imperviousness to injury by surviving the thugs beating the crap out of him with lead pipes and bicycle chains and not showing any reaction to getting scalded with boiling water or melting wax and talking all the while about how he "has a leg up, genetically speaking" because his grandaddy used to handle snakes in church and his granny drank rat poison for fun.
Then he gets his face barbecued and he cries like a bitch, and not only that but the screaming sound he makes is one of the most hilarious sounds I've ever heard from any actor ever.
If you haven't seen the scene I'm speaking of, go on youtube and watch it right now. You'll be clutching your gut to keep it from busting.