Well, way I see it, there are two types of challenging games: Those that make you restart the entire game after a certain amount of deaths (see: Battletoads, the NES Teenage Mutant Ninja Turtles game, Ninja Gaiden. Basically any challenging game from before the SNES era), and those that don't.

Since I personally find it hard and unfair to compare the two in terms of actual difficulty (and not just tedium or the time it takes to beat them), I'll just focus on the latter category, where you can die as many times as you want without having to play the first 10 levels of the game for the umpteenth time

I don't generally play that many really hard games, but from the top of my head:

I Wanna Be the Boshy, Super Meat Boy, Wings of Vi, Celeste - these four 2D platformer games all require precision and quick reflexes to varying degrees (Celeste being the easiest of them) but put you back in the action immediately after you die. I racked up thousands (possibly tens of thousands) of deaths in these games.

F-Zero GX - hardest racing game I've ever played. Ridiculously fast with damage from bumps and falls that can blow your vehicle up, ending the race instantly. Memorization and precision are required for the tracks, and then add reflexes on top of that to stop you from bumping into the 29 other vehicles on the track.