My favorite is turn based tactics/strategy and to a lesser extent RPGs. As a result I've been primarily a PC based gamer.
* Master of Magic – The oldest game I've played that holds up from more than nostalgia, still one of the most enjoyable turn based strategy games
* Deus Ex – My vote for the Citizen Kane of video games. The build systems, the multiple routes, the campy pulp fiction spy story that wound up having way too many true elements...
* Diablo 2 – click click click
* SMAC – My favorite of the official civ games. It's the first one where I feel they got the faction bonuses, government systems, and multiple victory paths working correctly. I also like the setting.
* Fall From Heaven 2 (full conversion mod for Civ 4) – The most complicated Civ-like. Completely different faction mechanics, a magic system, an alignment system, factions that subsume other factions, armageddion (victory or loss). I enjoy it but it's pretty far into grognard territory.
* Planescape: Torment – The best of the Bioware Infinity Engine games. Bizarre setting and fairly good writing.
* X-COM (remake) – I played the original but I slightly prefer the remake.
* Witcher 3 – The best RPG that's been made
* Divinity: Original Sin – Really good modern take on the Infinity Engine games. The combat system is particularly well done.
* Advance Wars – Really refined rock/paper/scissors unit balance. I really wish they'd release it or a remake for mobile.
PS + PS2:
* Carnage Heart – Fringe game where you program robots to fight using a visual grid/flow programming system. The cleverness comes from taking advantage of layout and control flow quirks to overload layout loops to handle multiple control paths. This let you get the latency/flow sophistication of later equipment on earlier tech and roll over the CPU. So many hours of math class programming on graph paper...
* Final Fantasy Tactics – Still my favorite turn based tactics game. Best story of the final fantasy games and one of the best combat systems out there. There is a mobile version of this but I wish the port was better and didn't spin wait the CPU.
* Shadow of the Colossus – There was a remake recently but the original is the most meloncholic game I've played