Strategy - faction/society simulator ~ Alpha centauri vanilla, pre-expansion.. although expansion is alright on its own, the game has been nerfed and rebalanced too much, IMO.
Strategy - turn based/historical ~ Romance of, Nobunaga, Hearts of Iron, etc etc. For those times when you want to be bored... micromanage EVERYTHING and be the dictator you truly are. Strategy.
strategy - tactics/SUPER detailed, SUPER grindy games ~ Final Fantasy Tactics, Disgaea at the top of the scale.
Persona games on DS, FFT A2, GEMFIRE! or FF12 revenant wings for lower impact... easygoing stuff.
Management games ~ entrepreneur, KAIROsoft games like game designer story, ninja village, etc, Aerobiz supersonic.
Real life simulators. You dont have a goal. The sky is the limit. You are dropped into the world and when you walk around you could find a glass cup, or a scrap of paper or some good guys.. so on.
Kenshi, Cataclysm Dark Days Ahead (Use a tileset like chesthole and be aware you ARE NOT supposed to survive... but the first 20-50 tries are there to teach you how to actually play teh game. Fuck tutorials.
),
Rise to Ruins, Rimworld (Those weird assed real life sims that look like carbon copies of that prison tycoon game.)
Super, SUPER casual games. Spades, minecraft, etc. games I dont mind playing after I took my sleeping pill and waiting for the lids to get heavy.
and I guess... those 'freemium' games that I have to keep coming back to actually get something done over time, cuz the world isnt going to solve itself by playing an hour here, half hour there, or five minutes during a trip. Fallout shelter, Rebuild 3, etc. Casual enough to pick up, addictive enough to stay for awhile... but nothing full-featured, story-heavy or anything.