In general I like games that are a good/interesting/fun abstraction of reality. This normally implies interesting mechanics and sugestive graphics. I normally prefer simulations, rpg, strategy and rogues. But never too realistic, unrelevant details should be wiped away, as an extreme example, what's the point of playing an ultra realistic simulator of a restaurant? It would be better to get a job doing that and earn some money.

Note also that I don't consider myself a gamer, I only play occasionally.

Yes, modern indie games are the only modern games I play.