Quoting: GuestDepends what people think of as a classic.

Very true. I was thinking something in 2000-2010 period. Go back before that, and things get really blocky and awkward real fast... I think I just carbon dated myself. :)

If you are into point & click, Full Throttle Remastered, If you prefer action, I would say Return to castle Wolfenstein but it's really personal choices.

EDIT : I second Unreal tournament, it's a classic in my book.

Bioshock 1 and 2 games fall in that range. And they make a nice companion to the native Bioshock Infinite.

+1 for Bioshock series.
There is always Oblivion and Mass Effect trilogy.
I've lost too many hours in all of them.

I stick to GOG games, but there are too many good ones there to list them all :)

Recently I tried installing Severance: Blade Of Darkness (it's one of the most challenging games when it comes to melee combat). Too bad GOG actually pulled the game from the catalog (but those who bought it still have it).

The Ur-Quan Masters HD is a freeware reimagining of 1992's Game of the Year Star Control 2, with native Linux installer.

Baldur's Gate was released back in 1998, and there is a new Enhanced Edition re-release, on Steam and GOG - with native Linux installer (Also Baldur's Gate 2, Icewind Dale, Planescape Torment, Neverwinter Nights)

The Elder Scrolls III Morrowind can be played with modern OpenMW engine and the original game can be found on Steam, GOG, Bethesda website (to get the game data files).

Quake, Quake 2, Quake 3 Arena are on Steam and GOG. Once game data files are grabbed you could play them with other game engines on Linux (or with WINE or Proton).

The full set of Serious Sam games can now be played via their new Fusion (2017) engine (It comes with the games) on native Linux. The old ones are Serious Sam 1 (2001) and 2 (2002), and on Steam and GOG. (Not sure about Fusion engine on GOG, because I own them on Steam.)

X-COM: UFO Defense was released back in 1993. Steam (Proton) and GOG (Windows only) have it. Likewise, X-COM: Enemy Unknown (2012) is in that series, but a bit later than you were aiming for (with a Linux installer) on Steam and GOG.

The original 2005 F.E.A.R. is superb. As is the 2007 Crysis and the even better 2011 follow up Crysis 2. If you like the Dishonoured series (and hence Arkane Studios), it's really interesting to try 2006's Dark Messiah of Might and Magic - great ragdoll physics and you'll recognise Arkane's hallmark level layouts and excellent voice acting throughout, even if the game is tiny bit rough by today's standards.

I'm pretty sure they all work pretty well under Proton, although the original Crysis needs some tweaks.

Aliens vs Predator and Bioshock

Freespace 2 - lots of mods to make it look better
Gothic 1
Risen 1
Mafia

Depends what games you consider "classic"

RTS
Most C&C games are locked to Origin , but give Tiberium Wars a try.
Company of Heroes 1
Warhammer Dawn of War 40k 1
Age of Empires 2 (and maybe 3)
Age of Mythology
Commandos series


RPG
Gothic series
Risen series
Baldur's Gate , Icewind Dale , Planescape Torment
Septerra Core , Gorky 17 (not many people i know played these but they are worth it in my opinion)
Fallout 1 , 2 , New Vegas

City Builder
Pharaoh + Cleopatra
Zeus + Poseidon
Caesar 3

TBS
X-COM
Civ 4
Heroes of Might and Magic
Disciples 2
Jagged Alliance

Stealth
Thief Gold , Thief 2 the Metal Age
older Hitman titles

FPS
Deus Ex (the one from 2000 - really worth it )
System Shock 2
Bioshock