Mine is a bit all over the place as I'm very fussy, but...
I generally prefer:
Simulation, in particular, Sim City 4, A-Train (which is a Japanese train network management franchise from Artdink), and Cities Skylines
Turn-based strategy: Fire Emblem, obviously. Because it's more about thinking, and I appreciate that I can easily interrupt a chapter when something comes up.
RPGs: Pokemon, obviously, but also regaining interest in Final Fantasy, and immensely enjoying Persona. They tend to have interesting world-building or good stories, not to mention I can easily interrupt a playthrough when I need to.
Anything that provokes my thought in regards to worldbuilding. Again, Pokemon, but also FE Binding Blade, and the Zelda franchise.
On the other hand, stuff that I avoid, unless if there are very good reasons:
Platformers: Partly because I'm not really strong in that dept, and also because of a particular franchise that I consider as overrated shit because of how the story in general is so brain-dead and and two characters in particular are spineless sissies. Odin Sphere, however, is a major exception.
Horror or too much gore. Though Yomawari may become an exception...
Racing: Though, F-Zero may become an exception.