1. Historical strategy games - this is a very small genre unfortunately, with basically only a handful really good games in it, like the Paradox-titles, the Civilization-series, Colonization and the Imperialism-games, but I just seriously LOVE it when they do this genre right, as you get to learn and relive interesting parts of out past, and also participate in challenging and fun gameplay. And no, this does not include tactics-games like Age of Empires etc.
2. 2D-plattformers - pure gameplay, quick gratification, no bad stories or other stuff that distracts from the experience, and when done right gives you just an incredible feeling of accomplishment when you beat them.
3. Action-adventure/rpg's - I am kinda cheating here by making this a pretty broad category were I include all stuff were your characters progress and get better, and also is action-based. So that include both stuff like Zelda, Castlevania, Metroid and Demons Souls. Like with the 2D-plattformers, the best games in this genre is about skill and pure gameplay, and gives great satisfaction when you overcome obstacles, without a lot of distracting stuff.