I find myself dying constantly in Donkey Kong. Although I don't have to pay money each time, it's still annoying to keep having to watch the intro each time.
I've tried pressing all buttons I could think of, so I don't think it's skipable, but maybe it is.
Same thing with Puckman/PAC-MAN.
On pinball machines, you can usually tell it to: "get on with it already!" by pressing a button, and so it would make sense for an all-digital game to also have such a feature for people who have already seen the intro a million times and just want to get on with the game.