Return to Castle Wolfenstein? The new Wolfensteins have quite a bit of story, but the old one is all skippable.
I’d have to recommend Untitled Goose Game, Goat Simulator, the Karamari series, and music based (do the thing to the beat) games like Dance Dance Revolution, Taiko Drum Master, Guitar Hero, etc.
If you’re looking for something arcadey and replayable, the Touhou series might be worth looking into. Great music, too.
So, so many. You're going to have to narrow it down a bit. Vagante is a great challenging roguelike platformer that's equal parts Spelunky and Dark Souls. There are recommendations for Factorio and Civilization here, which I wholeheartedly endorse. Mercenary Kings has minimal act break cut-scenes that are pretty short, but the gameplay loop is Mega Man crossed with Monster Hunter, and it works really well. Streets of Rogue is a highly systemic roguelike that really lets you go nuts with the sandbox, and it's got a great sense of humor at that.
As a bonus, all of those games are also fantastic to play co-op.
I played all you mentioned, except Factorio, and liked them, but never heard of Vagante. Looks interesting so I'll check it out, thanks.
I finally got superhot: mind control delete during the summersale. Very simple but engaging combat mechanic, and story is kept to a minimum
Played that quite a long time ago. Such a good game.
Ultrakill. Sometimes guys will talk to you, but its rare (only before bossfights), can mostly be ignored, and can be skipped after listening to it the first time.
Tetris
w40k Gladius?
I know Axiom Verge has a Speedrun mode that cuts out all the cutscenes, I don't know if that qualifies though, and you do kind of have to know what's going on outside of that. The story itself isn't necessary to enjoy the game though.
Disc room is such a fun game and it has almost no story
I hear ya, I hate when games have too much story. The stories are never any good and usually outright eye-rollingly bad. I particularly hate when they do "..."
Legend of Zelda, the very first one. Yoshi's Island. FIFA.
Victor Vran's not much for story but the game is fun. You can even find a weapon that launches exploding chickens.
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