Okay, this is kinda crazy, and I'm not sure it's considered a game, but every Saturday while I'm cleaning, I play music. The dogs have two favourite songs - one by Kid Rock called "Flyin High" and the other by Hinder called "Hey Ho"...(Yep, I'm 51 and I'm a rock and roll junkie!)
No matter where I am in the house when either of these songs comes on, they all come running, and start jumping on my legs. I pick them up one at a time, and dance around with them - the other two jump around in the floor on their hind legs dancing until I pick them up...They absolutely love it! By the time the song is over, I've danced with each of them 4 or 5 times!
It's funny, because music is going all day long, but these are the only two songs they respond to!
With Pedro, I also play 'fetch' with his favourite toy - a red rubber fish.
Gracie and Diesel aren't much into playing with anyone other than each other, but they love to dance!
My husband thinks this is hysterical, so when I'm not looking, their two favourite songs tend to shuffle around alot!