Well, I'd definitely have to say Survival Horrors and Psychological Thrillers. This genre is actually a sub-genre, seeing as though many of them are encompassed by other genres, but I digress.
Some people seem to not enjoy the feeling of helplessness as you struggle to reach the next checkpoint without running into any encounters that do you in, but I love it. In titles like Alan Wake, Amnesia: The Dark Descent, and so forth, I find myself scrounging for anything I can find, and I love that. Another great title would be Dead Space 2. I haven't played the third one yet, but the second one was a fantastic example of Survival Horror at its finest. You hear scratching in the walls before they pop out, you watch helplessly as people aboard the ship are killed before your eyes, etc. It's really a great game.
I'd also say First Person Shooters are great. Some of my favorite games are First Person Shooters - Bioshock Infinite, Borderlands, Portal, Half-Life - and really are just fantastic games. They're really not mindless games. I'm just getting into the Halo series, and I'm seeing just how much story there is to delve into.
Recently, I've also been getting interested in Platformers. It's far from my favorite genre, but it's a fun way to kill some time.
Turn-based RPGs are also great. Fire Emblem - which is a tactical, turn-based RPG - is fantastic. Off is currently my favorite turn-based RPG, with Pokemon at a close second. The original Final Fantasy was also a great game, but I'm still yet to have finished it, or played any of the sequels.