Takeshi's Challenge is arguably the hardest game ever made, period.

It demanded that the player sing for an hour without hitting any buttons, go through a side scrolling shooter sequence without ever going up, and you had to hit the final boss 20,000 times. The video above is a man going insane from playing. This game was made as a joke, as Takeshi Kitano hated video games, but ironically this is consistantly voted in the top 50 best famicom games ever.