Hmmm, that's a difficult question. I myself enjoyed this game that washed down the dump one time. It was called... Crossing Animals, I believe. It was a creativity-based game about building, exploring, and interacting with others. My favorite villager was named Sherb, as he reminded me of Azzy. I liked bullying any annoying villagers, =), but Azzy got upset when I did so, so I did it when he wasn't watching.
But as for a game to play WITH Azzy, I liked Super Smashing Fighters. Azzy mained a green lizard, while I mained an anime swordfighter. I liked playing it with him because it was fun to see his reactions and concentration, and it was a chance for me to release negative feelings in a healthy way. Of course, it didn't help much in the end...