I would say 3rd person action / adventure games, things like Batman AA & AC, Alan Wake, Sleeping Dogs, Gears of War, Giants Citizen Kabuto and the likes. This includes stealth type titles like Splinter Cell and Dishonored even though its first person.
Then it is things like the above but with RPG elements like Demons / Dark Souls, Vampire etc Also love the true 2d isometric RPG's like Silverfall, Baldurs Gate, IWD & Diablo
Then I would go for the tactical type games which covers Ghost Recon, Rainbow Six, Splinter Cell (again) and also games like Thief.
The above are always the ones I go for first regardless.
I do tend to play a mixture of all sorts, I occasionally play strategy games like C&C and DoW, however with those I tend to build a huge army and just stomp all over the map obliterating everything, not much strategy involved really!
I do like FPS, but I tend not to play them as much as I used to. Things like Borderlands get plenty time but I don't buy into the whole CoD and Battlefield craze. Can't be chewed with the multiplayer side of things and those games are now based around that side of things. Give me the original CoD and MoH over the newer iterations any day!