The S.T.A.L.K.E.R. series is generally the go-to franchise for immersive first-person games. Even if you don't consider them the best, they are pretty much unquestionably at the top of the league, at least when not dealing with the stupid glitches that plague the games if you don't have them all patched up. The Metro game are also a good place to go if you don't mind a little more linearity to the level design.
Amnesia: The Dark Descent is a good first-person horror game and arguably the scariest game you'll ever play. Even during the beginning, which is comparatively light on the scares, is still incredibly immersive and able to send chills up your spine.
As for the BioShock games, the first one is almost universally accepted as a great experience, provided you didn't play System Shock 2 beforehand. BioShock 2 and BioShock Infinite are a little more debatable, but I personally found most of BioShock 2 to still be at the very least enjoyable, and the first half of Infinite was great too. Whether or not you find the second half of Infinite enjoyable is hard to tell, as that's generally where the debates begin about whether or not the game is good.
Also, if you enjoyed Fallout 3 and Skyrim, then you should check out Fallout: New Vegas. I know there's quite a bit of debate between Fallout 3 and New Vegas fans about which one is better, with many claiming that only the one they like is good, but if you can put up with an excessive amount of deja vu, then New Vegas should still be a good game. If you already have Oblivion or Morrowind, you can check that out, but I've traditionally found the Elder Scrolls series to be very hard to move forward through, and even harder to move backwards through.
Also, while I know the Crysis series is really not known for being great, I found Crysis 2 to be an excellent game.
Amnesia: The Dark Descent is a good first-person horror game and arguably the scariest game you'll ever play. Even during the beginning, which is comparatively light on the scares, is still incredibly immersive and able to send chills up your spine.
As for the BioShock games, the first one is almost universally accepted as a great experience, provided you didn't play System Shock 2 beforehand. BioShock 2 and BioShock Infinite are a little more debatable, but I personally found most of BioShock 2 to still be at the very least enjoyable, and the first half of Infinite was great too. Whether or not you find the second half of Infinite enjoyable is hard to tell, as that's generally where the debates begin about whether or not the game is good.
Also, if you enjoyed Fallout 3 and Skyrim, then you should check out Fallout: New Vegas. I know there's quite a bit of debate between Fallout 3 and New Vegas fans about which one is better, with many claiming that only the one they like is good, but if you can put up with an excessive amount of deja vu, then New Vegas should still be a good game. If you already have Oblivion or Morrowind, you can check that out, but I've traditionally found the Elder Scrolls series to be very hard to move forward through, and even harder to move backwards through.
Also, while I know the Crysis series is really not known for being great, I found Crysis 2 to be an excellent game.
