I'd like to disagree on the simple bit
I have no favorite genre altho I have favorite games per genre and per age There are old gen games that inspired new gen games but I still love em all.
RPG:
Multi player old gen - Diablo 2 Lord of Destruction
Multi player new gen - Guild Wars 2
Single player old gen - Gothic 2
Single player new gen - Dark Souls series, Witcher series, Fallout series
RTS:
old gen Red Alert 2 Yuris Revenge haven't found a RTS game worth mentioning since then.
Turned Based Strategy:
Heroes of Might and Magic series and Civilization series
FPS:
old gen Counter Strike
new gen Rainbow Six Siege
Horror genre:
Have you ever played Alien Isolation in a dark room at night alone on a massive projector screen while high? no? try it I dare you
same goes for some of the Resident Evil games, Silent Hill games, Outlast games, The Evil Within games, Last of us...
Adventure genre:
new gen - Life is strange - that game is awesome
Fun little multiplayer games: Worms, Tekken... and so on