Walking around, I get to see a lot of pets. Small dogs are the top choice. They're cute, portable, and can be accessorized. See also: Paris Hilton.
Cats are loved more in Japan, but you can't really put a leash on them and take them around town. There are plenty of cat cafes, cat-themed merchandise, and cat costumes. And occasionally, you'll see a pet cat in a window, taking a nap. There are plenty of stray cats around town too.
By the way, I should be back in Tokyo by now. I'll get back to my Kansai posts soon!