Only 2 come to mind for me.
Snake's Revenge for NES ( My friend wanted it back. I wonder, was the last boss invincible? If I had more time, I might have done it.)
and
GTA London 1969.
I think that whole bloody game had you do it all for nothing. It tells you to kill the Crisp brothers then leads you to an arrow where there is nothing. If there was a way to complete that, it sure as hell fooled me, and I tried several times, always the same result.
Anybody beat those, or are they truly impossible?