There are entire genres that I think in many ways have passed younger gamers by.

Point and click adventures were the biggest thing in the world at one point. The classics are the Lucas Arts entries, like Indiana Jones and The Fate of Atlantis, The Dig (both based on unused Spielberg pitches), the Monkey Island games, Full Throttle, Day of The Tentacle and Loom. You've also got Myst and Riven (Riven being the far superior of the two), and my personal favourite, The Longest Journey, which has an absolutely stellar story and really compelling protagonist with a lot of depth to her. Also, positive queer representation in a nineties game, holy shit.

The next lost nineties genre is the space sim. The kings of the genre were Wing Commander and X-Wing/Tie Fighter. Then you've got Privateer and later Freelancer. For the Wing Commander games read a summary of 1 and 2, then jump in with 3, the first to feature FMV with Mark Hamill as the player character (genuinely an excellent performance too, he took the role really seriously and saw it as every bit as important a scifi property as Star Wars). John Rhys Davies (Gimli) and Malcolm McDowell also make appearances.

And of course, the classic nineties FPS, a genre that feels very, very different from modern FPS games, though there have been some good attempts to recreate it. You know Doom, and Wolfenstein 3D (the latter does not hold up; the former absolutely does), but also check out Heretic, Hexen, Rise of The Triad, and most importantly, IMO, the Marathon games. These were the precedessors of the Halo series, and they combined really solid action with a genuinely amazing story. It's the kind of big, high concept that you rarely get in movies, TV shows and games, with a world that the writers clearly put a tonne of thought into, and some characters who will stick with you long after the game is over.

Finally, some stuff that doesn't really fit any of the above. Crusader: No Remorse and Crusader: No Regret are isometric action shooters with some fun storytelling and LOTS of explosions. If you get them on GOG be sure to download and read all the supplementary material, it really fleshes out the world and the characters. System Shock probably doesn't even need mentioning with the recent remake, but the originals truly hold up, especially with the UI and controls polish Nightdive added. Syndicate and Syndicate Wars are very hard to explain, but they're really fun (That said, I'll give an even stronger recommendation to their modern spiritual successor, Satellite Reign, which deepened the gameplay significantly while still retaining all of the spirit).

There's plenty more, obviously, but that's what immediately comes to mind as worth checking out.