Age of Empires and AoE2
Borderlands series
Star Trek Online (F2P)
Super Mario Brothers series (ending at Super Mario World)
Starcraft series
Command & Conquer series (excluding C&C4)
Mass Effect series
Deus Ex series (yes, I do include Invisible War in this)
Battlefield series
Medal of Honor series (ending at MoH Airborne)
Far Cry 2 & 3
The Elder Scrolls series
The Fallout series
Half-life series
Portal series
Saints Row 3 & 4
Space Pirates & Zombies
Starpoint Gemini 2
Freelancer (especially with mods)
Wasteland 2
Age of Mythology
Total Annihilation
Assassin's Creed 2-4
Avernum series
Bastion
Brink (severely underrated game, designed for MP)
X-COM series
Company of Heroes
Eternal Silence (HL2 MP mod, awesome)
Geneforge series
Just Cause 2
Left 4 Dead series
McPixel
Quake 2
Red Faction Guerilla
Shadowrun Returns
Civilization 3 & 4
Alpha Centauri
Civilization Beyond Earth
Sins of a Solar Empire series
Supreme Commander series
Ghost Recon series
Rainbow Six series
Torchlight series
Tribes series
Earthsiege series (abandonware)
Cyberstorm series (abandonware)
Stellar 7 (abandonware)
Mechwarrior series
Mechcommander series
UFO series
Dawn of War series
Halo (the original)
H.A.W.X.
Shadow of Mordor
Minecraft (on a private server with mods)
Omerta - City of Gangsters
Organ Trail (only after playing or watching a playthrough of Oregon Trail)
Pixel Piracy
Prototype series
Star War Knights of the Old Republic 1 & 2
Star Wars Battlefront 1 & 2
Star Wars Empire at War (with or without expansion)
Star Wars Jedi Knight series
Tyrian 2000
Age of Wonders 2 & 3
Rise of Nations - Rise of Legends
Tropico Series
World in Conflict (it's a RTS version of Battlefield Bad company or the 1984 version of Red Dawn)
Legend of Dragoon (the female character literally has her clothes explode off her when she transforms)
Pokemon series of games for the GBC and GBA (denoted by different colors)
Battletanx (for the PS1)
Star Wars Shadows of the Empire (for the N64, can't be emulated)
Earthbound (for the SNES)
Teenage Mutant Ninja Turtles 4 - Turtles in Time (for the SNES)
Zelda - A Link to the Past (for the SNES)
Starfox (for the SNES and the later one for the N64)
Rome Total War
Stronghold series (some are better than others)
FlightGear (free, open source, high-detail flight simulator)
That's my current short list that I've intentionally left out a lot of old DOS titles from. (I tend not to include many abandonware titles if I can help it, as they're usually very difficult to find and run)