I own thirteen, although I'm probably going to let go of a couple of them. They're mostly physical copies but I have a couple digital games too.
Physical:
Animal Crossing: New Leaf
Animal Crossing: Happy Home Designer
Dragon Quest VII: Fragments of the Forgotten Past
Dragon Quest VIII: Journey of the Cursed King
One Piece: Unlimited World Red
Pokémon X
Pokémon Y
(planning to sell because I don't feel like I really need both)
Pokémon Omega Ruby
Pokémon Ultra Sun
Pokémon Mystery Dungeon: Gates to Infinity
(also planning to sell because I really didn't like it )
Pokémon Super Mystery Dungeon
Digital:
Fantasy Life
Style Savvy: Styling Star
I'm not normally one for digital copies, but Styling Star was digital-only in North America, and I couldn't find a physical copy of Fantasy Life that wasn't ridiculously expensive. ;u;