I will stream just about any game. I am very eccentric when it comes to games. I play FPS, MMO, RPG, Action, Puzzle, Card, and TPS games. I will occasionally play the turn based game as they hold a special spot in my heart (Final Fantasy Tactics) but rarely do these days.
My first go to when I want to be able to casually play a game not knowing how much time I have to play would definitely be League of Legends. Who can say that game is not fun? I have more fun learning that game than any other game I have played in the last 10 years.
When the Division comes out I am sure that will take a majority of my stream time as it was anticipated by me for years and from what I see it will be a graphic intense game filled with new systems untraditional from other games.