I don't have the one favorite game, because I play different types of games and all are equally appealing depending on my mood. Here's a list of favorites:
(1) Roleplaying: Planescape: Torment (1999)
The only game where I could have philosophical debates and they felt convincing. Also, hauntingly beautiful music, unusual fantastic setting. Too bad it didn't age gracefully.
Honorable mention in this category: Fallout 2, Arcanum, Fallout: New Vegas, Dragon Age Origins, Knights of the Old Republic. RPG quality has sharply declined with the advent of fully voiced protagonists, and hasn't reached the heights of the turn of the millennium again. DAI went in the right direction, but didn't do enough to make it into the list. Get rid of the paraphrasing, Bioware, and your next game might make it.
(2) Strategy and Tactics (turn-based): XCOM: Enemy Unknown/Enemy Within (expansion) (2013)
It should be enough to mention that I put 600 hours into this. Intense, challenging, emotionally satisfying. Also, one of my all-time favorite NPCs in Dr. Vahlen, and my most emotional moment in strategy gaming: the unveiling of the first Firestorm interceptor still gives me the shivers after more than a dozen games, with Shen's perfect dry comment "I think we've just leveled the playing field". XCOM 2 has superior gameplay and customization, but remains behind its predecessor in story and mood.
Honorable mention: Sid Meier's Alpha Centauri (1999), Age of Wonders series, the old Microprose classics Master of Orion 1 and 2 (3 doesn't exist) and Master of Magic (1993-1996). Also Battle Isle 3: Shadow of the Emperor.
(3) Strategy and Tactics (real-time): Spellforce: The Order of Dawn and its two expansions (2003-2006).
This is actually a genre mix of RPG and RTS, with neither part done exceptionally well and excessively bad voice acting for everyone but the Rune Warrior (the protagonist), but the story was fantastic and the (female German) Rune Warrior's VA is still my yardstick for excellence because it's the only voiced protagonist I know who could express heroic determination without turning into an ideologue.
Honorable mention: Starcraft: Brood War. Kerrigan and Zeratul are awesome.
(4) Simulation games: Anno 2070
A nice SF- and ocean-themed addition to the Anno series. Complex without being finicky, and moddable. Disadvantage: it's player-harassing Ubisoft. It should say enough that I bought this game in spite of its publisher and didn't regret it in spite of the expected annoyance factor. Didn't buy anything from them before and after.
(5) Action/Adventure: Tomb Raider (2013 reboot).
The first game of the franchise that grabbed my attention since 1997. Didn't like the QTEs, but the game was atmospheric and very intense. Bought the sequel last month but couldn't get into it yet.
(6) Stealth-based games: Thief 1 and 2 (1998-1999)
I still play these now and then. No other game of the type, or later one of the series, captured their mood and their sheer intensity.
Honorable mention: Thief (2014). Extremely well-done technically, captures the mood of the City well, but lacks in player freedom. Also: Alpha Protocol.
(7) Sandbox games: Minecraft (modded).
Probably the game I've spent most time with over the years. It should be noted that modded Minecraft is to vanilla like an automated factory is to a hammer. The potential feels unlimited in spite of the primitive visuals. In no other game can I be as creative. Designing and building complex systems and beautiful structures is the name of the game.
(8) Action/Story-based: Deux Ex series
This is one of my most favorite game series, starting with Deux Ex (1999) because it's about one of my favorite themes. I usually play these as stealth-based games but you needn't, so they don't belong in that category, and they have rpg elements but not enough to turn them into RPGs. DX: Invisible War was an excessively bad console-to-PC port though, so don't start there,