Half-Life is the game that made shooters tell stories. Valve released it in 1998, and instead of levels separated by menus, it dropped you into Black Mesa as Gordon Freeman, a physicist in a hazard suit, and never once took the camera away from you. The famous tram ride at the start, the resonance cascade, the crowbar, the headcrabs and the soldiers sent to clean up — all of it plays out in first person, continuously.
This page runs a browser port of the original. It's a 1998 game, so it runs comfortably in a tab, and it holds up: the pacing, the level design and the enemy AI were decades ahead of their time.
This page runs a browser port of Valve's 1998 original. The full game is also sold on Steam, where it's frequently free or heavily discounted.
It told its story entirely in first person without cutscenes, gave enemies genuinely smart squad behaviour, and mixed shooting with environmental puzzles. Almost every narrative shooter since borrows from it.
Crouching while jumping tucks your legs up and gains extra height — required to reach several ledges in Half-Life. It became a standard technique across the whole genre.