Forget the Bioshock series imo, and play System Shock 1 and then System Shock 2. It is important to play them both and in the right order because the gameplay is better in the first game in some ways, and better in the second in other ways, and also the story is so much more shocking in the second game if you have played the first. You need to get the right versions/mods to make them playable today, the first game especially because it was released before games started using mouse look. But they are must play games because nothing since then has done as much in terms of gameplay. Bioshock might have pretty modern graphics, but every single aspect of its gameplay is inferior to the System Shock games. And even today there are no action FPS that I know of which have as many items in terms of ammo types, weapons, and grenades.
Also to me, Arma 2 or Arma 3 is a must play game, if only to experience how huge the scope is. Games like Call of Duty and Battlefield are just toys in comparison. The Arma games have dozens of weapons, each handle realistically with correct ammo, and you can crouch, lean, lie down in the grass, roll in the grass to flatten it, etc. It is a shooting simulation, bullets drop over distance, you can correct the rifle sights, etc. And the locations, forget about running in one direction and hitting, "YOU ARE LEAVING THE GAME AREA!!!!" messages, because the regions you play in are the size of entire cities or even countries. In Arma 3 the big map is 270 km2. And then in addition to all this, there is a whole series of vehicles, dirt bikes etc, then humvees, gun trucks etc, and then a whole selection of tanks which are incredibly fun to play with, and then a whole selection of choppers and jets, both combat and utility. In multiplayer you can air lift a tank or ambulance or something to places that need it, and play as a genuine pilot, or you can get in a gunship or fighter/bomber and fly around causing mass destruction. It is really amazing.
Also, Baldur's Gate 2. The first game is good too but it is a low level RPG so there is a lot of meleeing wolves with some basic magic. If you want really deep and challenging tactical battles, then Baldurs Gate 2 is hard to beat. It can be hard to enjoy these days if you are looking for something action packed, but if you can get into the spirit of slower paced and tactical gameplay that really challenges you and has a lot of story too, then it is as good as it gets. Dragon Age Origins is a lot simpler and less deep and challenging, but still pretty good and yet it has better modern graphics and better viewing angle etc. So if might be a better place to start because it is easier to get into, and then if you enjoy that and would like something deeper and tougher, then try Baldur's Gate 2.
Also, Command & Conquer: Tiberian Sun. This was made free for a while recently, but that might have ended by now. There are countless RTS games to choose from and some good ones are mentioned in the thread, but imo this one is the best, and it is also unique in how it plays. The problem with the likes of Supreme Commander is that it devolves into a rush of spamming out millions of units and capturing as many resources as possible and it is all quite manic and intense and I don't like that. There are a lot of games which are the opposite too but they can be a bit tedious. For me Command & Conquer: Tiberian Sun is the perfect mix of both. It is big enough and you can do well with fast clicks and decisions, but ultimately it is down to smart decisions and clever attacks. You can't just send a swarm of tanks to flatten your enemy's base because they will just hit them all with an EMP and then kill them all while they are disabled. You can't just send a bunch of engineers to capture everything because they can build concrete slabs / artillery / emp / lots of stuff to kill them and waste all your money. You can't just send 20 bombers to flatten them because they will just build a bunch of SAM sites to shoot them all down. You have to attack in a smart way and with a mixture of these things and preferably while distracting your opponent. I've never played an RTS that has quite as much depth as this game.
Also, Portal, Dune 2, Syndicate, Atomic Bomberman, Lemmings 2, Worms World Party, Duke Nukem 3d, EverQuest (p99), Jagged Alliance 2.
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