Usually here some old titles, but my personal recommendations are Quake 3, UT2004 and Skyrim.

Must check

dhewm3 has demo support and link to it

Webliero  online Liero gmae

Classicube  - optimized minecraft written on C#, mp and mostly classicmode only

Lichess Free online chess mp and cpu. This is so far best online implementation

https://jstris.jezevec10.com  Tetris online, has everything, even mp

https://gtaconnected.com   GTA 3; VC; SAN - sp in mp! Needs original gmaez ofcourse.

Super Mario War pretty fun mario themed game especially for more than 1 player

Free

http://mmr.quarkrobot.com  Lode Runner improved, has mp

Little Fighter 2 Great 2D fighting fun game, has coop and mp. Also online implementation  http://project-f.github.io/F.LF/ 

Postal 1  (NOT REDUX but re-release of Postal 1 with online coop and all official maps including japan ver) Strongly recommending to play without annoying voices, it's possible to turn them off atleast. And slightly raise up difficulty. Also if decide to play online, be sure to use my patch.

http://www.amuletsandarmor.com/  - old ported to win rpg with coop

WinUdav - super old snake variant for windows but with improved gameplay and mp

library-of-blabber - infinity library

BabaIsYou (old) - fun puzzle gmae

Gate88  - interesting gameplay idea, reminds TD and strategy with action

Savage: The Battle for Newerth - great game of TPS/Shooter/Strategy and a bit RPG but might be super hard for beginners.

Sonic Robo Blast 2 - Sonic is back!

Clonk c00l 2D fun

Tunnel Runner Redux  Great remake of an old atari game, also avaliable for android

Echoes+  - fast game

SuperMarioBrosX and SMBX2 - Mario 2P gmae

Facade - You enter to their house as guest and say mashed potatoes, after that you get kicked off

lixgame  Serious very good remake of Lemmings, with it's own enchanced gameplay and online multiplayer (lobby exists)

https://gtamp.com/gta2/  Much improved gta 2


Demo versions

Enemy Territory: Quake Wars - for comfortable playing, recommend to disable DPI scaling in .exe proporties and check https://www.pcgamingwiki.com page of the game, com_unlocktimingMethod should be set 0 instead of 1 to get more than 30 fps, also it works only in LAN/internet for weird reasons, atleast possible to set in demo server aswell.

Q1:

Crashday  Absolutely fun crazy racing,demolishing derby game! Demo also has mp. It's so epic! Steam has remastered version aswell

Fury3  Great gameplay

Hellbender  Next after Fury3. Comes with better graphics and more dynamical hard gameplay + mp. Both series are brilliant. Demo is also mp

UrbanAssault  

Rollcage Stage II  Pure fun racing game, there is also somekind of racing defrag mod(scramble or smth) 

ODT  Very good action tps game

GEX 

Zapper 

Montezuma Some places even reminds DeFRaG where you need to jump, or avoid smth 

Dark Vengeance  Pretty fun simple adventure slashing game. Reminds Rune and Hexen 2. The demo has mp aswell.

Sponge Bob Quest  (rus version in ag.ru)

Gun-Metal-Demo player controls powerful robot which can be transformed into flying machine. Massive action. Demo version is short but still great. 

Recettear  anime rpg game with trading

On win 7 64bit I couldn't play any mode there, blackscreen. 

WWP pallete glitched totally even patch not working (and tcp/ip pwnd there aswell)Â