I think the problem with recommending games is time, in so much that progress marches on and the games that wowed me decades ago (literally) now look and feel exactly what they are; dated.
So some of the games that I have been blown away by, for various reasons or just really loved and not in any particular order (you will notice a very FPS orientated list as FPS is my 'thing':
Tomb raider PS1 - going from a Sega Megadrive to this was astounding, both in terms of gameplay and visuals.
Quake - full 3d models and fast paced, exciting gameplay was a massive leap from the 2d Sprite games previously offered. Plus it had a banging multiplayer. I was a teenager and falling in love with PC gaming. I spent a lot of time quaking!
Unreal - wow just wow. This game was the mutts nuts when it was released. It also came with it's own level editor UnrealEd which was based on the awesome level designer Worldcraft by Ben Morris.
Half Life - for its day it was superb in story, gameplay and visuals. It was the seminal first person story shooter.
Resident Evil - still a fine game even now. Trying to do speed runs to get the special weapon was also fun. But god damn the camera angles mixed with hardly any ammo and low health made it exciting.
System Shock 2 - eerie, scary and hard. It was my first experience of an rpg shooter.
Deus Ex - as good as SS2 was, deus ex took it to a whole new level for me. I fell in love with the series and have every release since, although some are better than others! I'm looking at you DX invisible war!
FFVII - straight up the first game that bought a tear to my eyes. Superb story telling and probably one of the best games ever made.
Morrowind - my first experience of an open world fps RPG and it was awesome. The art direction, gameplay, music and story gave me plenty of happy hours.
Lego games - specifically Indiana jones 2, hobbit and Jurassic world. Fun, easy going games with plenty of humour.
Command & Conquer Generals - brilliant RTS game with a great multiplayer. I'm always sad to see the demise of both the C&C franchise and the rts genre in general.
Quake 3 (and the threewave, ra3 and OSP mods). What can I say. This game is ingrained into my gaming DNA. I have spent thousands of hours playing it. As a multiplayer experience I love it. As a game it was ahead of it's time. The movement and physics are awesome. Gunplay is great and you get better or quit. No hand holding. No crutches. I still wander back to QL now and again to play with a few old quaking buddies of mine. I would play it more but dont have the time to invest in it these days. It takes effort not to be cannon fodder!
Tribes Ascend. This game was awesome. Dead as a dodo now but back in around 2011/2012 I started playing this. Didn't have a clue. Many times my arse was handed to me. Huge learning curve but so rewarding. Met some awesome people playing this too who really helped me improve my game
Never got better than average but loved it. The game had so many facets and I genuinely find it remarkable it didn't do any better. Well I kind of know why it didnt because the dev sold out to a microtransaction model with a different IP. If this had have had the right marketing and investment, I reckon it could have been a popular esport. TA still has servers up but its hit and miss if you can get a decent game. Worth it when you can though