If you want a great platformer with amazing graphics, look no further than Crash Bandicoot.
As the story starts out, you will see Crash in Dr. Neo Cortex's lab, having some experiments done. It will kinda seem like a dream, because you will wake up on a beach laying face flat on the ground, beginning the first level. And this where all of it starts, the classic first scene of the classic platformer.
Another thing everyone would not would be the Motley cast of bosses which Crash games have about 15 appearing in many of his titles, all having special powers and weird personality's, some being completely insane, some being calm but secretly insane. So in the end you could say they are all insane. Including all the scientists. When you play the game you will see what I was talking about. :)
So with all the bosses and enemies, you will want to know what the levels and worlds are like. Which I have to say, the first game was the most unique. With the 'overworld' view, and three islands to go to, it made the game every bit more exciting, which can be easily backed up by anyone. Though some of the levels are repetitive and look the same, the formula still makes it strong through the whole game. But I have to point at one more thing you will see THROUGHOUT the Crash series, especially in this very title: extreme difficulty. Some of the levels and puzzles are the hardest ones I have encountered ever. I played this over and over when I was a kid because of how hard the game freakin was.
But aside from that, Crash amounts in the end to an awesome platformer, great graphics, and anything else you want to see in an old school platform. (Including bosses whose butt cracks hang out ;)
One more note: the controls. They are excellent and dont take much time to get used to. Just adds to the great game.