This is very much like movies.  I enjoy Role Playing Games, Action, Adventure types with purpose.  I'm not a huge fan of the first person shooters, but I did enjoy DOOM and Quake in their day!  I like games where I can think and it changes as you play the game.  Something where time passes or there are rewards.  I enjoy the occasional Solitaire too though!  I want something to not make me think too much and that is quick.

I am currently playing World of Warcraft because it offers quests that you can complete and get rewarded for doing.  Some are quick, others take more time.  But it's a progressive game.  The downside is there is not a real end to it so I don't have anything to look forward to.  I'm also playing Zelda Twilight Princess on the Wii and enjoy this a lot too, but its direction isn't so obvious.  I like having objectives laid out for me to complete.

I can get really good at a game if I play and practice it, but I don't do that so much any more.  I don't have the time!  I remember when I was young and Nintendo 8-bit was new and we would beat game after game and track them to see who beat the most.  I had over 200!  Today’s games have lost their appeal for me to do that or maybe it's that I have done it so long they're not as enjoyable.