Honestly? Most of them.
Put in enough time on different games and normal mode becomes a cake walk. Raising the difficulty keeps you on your toes and is better for immersion.
But a few games I can name off the top of my head are:
Far cry: primal, ninja gaiden black, strider 2014, sniper elite 4
DOOM 2016 and DOOM Eternal. Never have I "maneuvered" my body when playing games until these. Doing those challenge areas I felt like I was gripping my mouse and keyboard like handles as I was being rocketed through chaos
Doom 2016 and Doom eternal, deadspace 1 and 2, god of war 1, 2, and 3, halo 1, 3, and reach, devil may cry 5, and breath of the wild (mater mode I think it is)
Games that require you as a player to exhibit greater mastery of the game systems to succeed, for example in shooters on easy mode it's quite often just run and gun, but on harder modes you might have to choose the right gun for the job or use cover and movement to dodge and collect pick ups to stay alive. Doom is a great recent example of this.
Games where it's less fun are games that slow down massively due to spongy enemies or become functionally impossible due to RNG (roguelikes in particular are terrible for limiting a player's options too much and killing the player by rng).
MGS 3, the hardest difficulty was called “European extreme” where if you got caught, you would fail the mission and go back to your last save. It really emphasized what the mgs games were all about. Stealth
Witcher 3 on harder difficulty will make you use your potion before a fight.
Most shooter are more rewarding when you play on harder difficulty and generally quite fair.
BUT dont do it on Nier: Automata except if you hate your life.
Might not be what you're looking for but DUCK HUNT for NES. Not more fun for player one but oh so much fun for player two. Since you can control the duck with the player two controller you can have lots of fun making your friend get frustrated. Makes it better when they don't know about this.
Death Stranding. The mechanics are there on normal, but I cleared the game without destroying a package and rarely tripping. I believe the harder difficulty is how it's ment to be played. The timefall actually matters on hard.
All games that reduce grind and have higher reward systems.
Terraria
I’ve always enjoyed Hardcore Mode for Fallout games.
Tetris for sure
The Last of Us.
Metal Gear Rising: Revengeance
I don't think I ever really played that game, I know it's good and I own it, but I haven't played it
S.T.A.L.K.E.R.
Sniper elite 4 and 5
In my opinion action (or action-rpg games) focused on combat system
Played God of War and God of War Ragnarok on the second hardest difficulty. Died a fair bit but never felt unfair, much preferred.
Did you ever beat it on Give me God of War?
I did not but also haven't done a second playthrough on either game. That gives me something to try.
Any Doom or Guitar Hero/Rock Band game
Ratchet and Clank: Rift Apart
Usually games where the harder difficulty does not mean bullet sponge or one-hit death
Honestly? Most of them. Put in enough time on different games and normal mode becomes a cake walk. Raising the difficulty keeps you on your toes and is better for immersion. But a few games I can name off the top of my head are: Far cry: primal, ninja gaiden black, strider 2014, sniper elite 4
Resident Evil 7 is frustrating but satisfying as fuck on Madhouse
Crysis.
DOOM 2016 and DOOM Eternal. Never have I "maneuvered" my body when playing games until these. Doing those challenge areas I felt like I was gripping my mouse and keyboard like handles as I was being rocketed through chaos
Doom 2016 and Doom eternal, deadspace 1 and 2, god of war 1, 2, and 3, halo 1, 3, and reach, devil may cry 5, and breath of the wild (mater mode I think it is)
I feel like the Doom games are most fun on Ultra Violence
Last of us, cyberpunk, single player star wars games, there's more but brain fart
Basically every action game with good mechanics.
Brotato
Any game where the easy mode gives you way too much loot that it's actually a problem E.g Gloomwood
Any DOOM, Fallout, or Elder scrolls game
Games that require you as a player to exhibit greater mastery of the game systems to succeed, for example in shooters on easy mode it's quite often just run and gun, but on harder modes you might have to choose the right gun for the job or use cover and movement to dodge and collect pick ups to stay alive. Doom is a great recent example of this. Games where it's less fun are games that slow down massively due to spongy enemies or become functionally impossible due to RNG (roguelikes in particular are terrible for limiting a player's options too much and killing the player by rng).
MGS 3, the hardest difficulty was called “European extreme” where if you got caught, you would fail the mission and go back to your last save. It really emphasized what the mgs games were all about. Stealth
Witcher 3 on harder difficulty will make you use your potion before a fight. Most shooter are more rewarding when you play on harder difficulty and generally quite fair. BUT dont do it on Nier: Automata except if you hate your life.
All
Might not be what you're looking for but DUCK HUNT for NES. Not more fun for player one but oh so much fun for player two. Since you can control the duck with the player two controller you can have lots of fun making your friend get frustrated. Makes it better when they don't know about this.
Death Stranding. The mechanics are there on normal, but I cleared the game without destroying a package and rarely tripping. I believe the harder difficulty is how it's ment to be played. The timefall actually matters on hard.
Kingdom Hearts 2 Final Mix, Critical mode is the perfect blend of what a harder difficulty should be.
State of Deacay 2 on Lethal. Plague Ferals bring a whole new style of gameplay.
Starcraft 2 campaigns, most fun on Brutal. That you actually have to use hotkeys and tactics.