Probably a toss up between Double Dragons and Battletoads.

I'm gonna say Oddworld: Abe's Oddysee.

ninja gaiden (XBOX) OR FEAR on toughest difficulty on 360

 I second this, that game is incredibly hard.  I doubt anyone ever beat it.

There won't be more than three people in the world left who will have any idea what I'm talking about but at one time text only games were popular. Zork was the first well known one. A company called Infocom specialized in them and they could be tough.

One in particular, The Hitchhiker's Guide to the Galaxy (1984, Steve Meretzky & Douglas Adams) had a particular puzzle to get the Babel Fish. That puzzle was so elegant and mutilayered that whether or not you could solve it depending on exactly what objects you had picked up going back to the beginning of the game.

I never found a tougher puzzle in any game since.

Ninja Gaiden on the NES what the hell was Mr Itagaki's mind going through when he made these games?

The Animal Crossing Series.

F Zero GX story mode.

Super Monkey Ball Banana Blitz or Battletoads.

as i remember ,,it was ninja gaiden on original xbox ,,,,it was not a good/satisfying hard game but it was rather frustrating and unforgiving,,,that game was the only game in my last gen collection, as I remember ,that I didn't finish