LogFAQs > #967436837

obvious answer I guess is Star Fox. maybe not strictly plot.

there are other games like Buster Bunny SNES where there are additional levels on the higher difficulties.

there are some games like GoldenEye or Thief where the mission objectives change with difficulty, but that's definitely not plot. Star Fox is a lot closer to a plot change than those.

there's almost RE2 where you can choose which character takes which path at the start. not sure if counts as difficulty though.

you could think of any RPG with a branching storyline (if there is such a thing and that's not just a pipe-dream) as being close to this, but sort of the reverse. it's not the difficulty changing the plot, it's the plot changing the difficulty.