My favorite when I was in graduate school was Farmville. I would plant or harvest in between reading or writing or posting in my classes. When Bejeweled came out I played that and tried all the variations, too. I still play Bejeweled Blitz once in a while on my phone. I love the one minute games that allow me to play as much as I like but give me a stopping place, too.
My current favorites are Candy Crush and Farm Heroes. They have the short levels that I like and challenging puzzles that keep me interested.
I also have a free Sodoku game that I make myself play every week. I don't enjoy number puzzles very much, but I read that doing them is good for your brain. I can do it and if I pay attention, I can get a fairly good score.