This is a difficult one, and I find myself torn between three answers. I do love strategy games and RPGs, but the winner has to be the adventure genre. I’m a sucker for a good story, and the classic adventures from Lucasarts, Sierra and others deliver that consistently. I also love puzzles, which these games also tend to embrace.
In terms of individual titles, I love the Discworld games, as well as Lucasarts classic such as Monkey Island, Grim Fandango, Day of the Tentacle and Full Throttle. From Sierra, I loved the first Gabriel Knight game (before all the FMV), Space Quest and King’s Quest. Other favourites include the Broken Sword series and Pendulo’s Runaway series. I also have a lot of time for Telltale Games and their various offerings, though I’d prefer to play more 2D adventures in the classic style, rather than their (admittedly beautiful) 3D games.
I think that the best thing about these games has, for me, been the humour. It’s interesting that the genre developed in that way, focusing so much on producing comedy. There are exceptions, with games like Phantasmagoria focusing more on horror and drama, but I’ve never really like those games. I’ll keep my funny stories!