I know why I play games. It is not just "because they're fun"; that's a crummy answer that doesn't really say anything. I play video games because all of my friends lived miles away from me, some even in other cities. What else can a poor boy do?
I grew up on Nintendo consoles, having everything from the NES to the Gamecube at some point in my life. Now, I am a PC gamer with a reasonable Steam library, a love of GOG and indie games, and a mechanical keyboard by eMachines from a time before laptops were everywhere.
The games I like generally have some immediacy to them - games that feel good to play or offer something that I determine to be satisfying.
Favorite games in no order: Shadow of the Colossus, Mark of the Ninja, Dishonored, Star Fox 64, UT 2k4, F.E.A.R.
I have many other games that I love to death, but these stand tall in my mind.
Genres I could never understand or get into are turn-based RPGs, most MMORPGs, and Sports games.