My ex has stolen my dog that is legally mine. She is registered under my city under my name. How can I get her back?

I write this as a dog-lover, but unfortunately, our laws treat pets as property (grrrr). So the only practical way to retrieve an "item" that was taken from you (outside of the police, who probably won't help) is to file a lawsuit, either in small claims court/district court or superior court. 

The question will center on ownership. You may be the licensed/registered owner of your dog, but if you were in a relationship and your ex took the dog as part of a split, be prepared to prove ownership outside what you describe. Be prepared with vet bills that you paid, vet visits that you took your dog too, and anything else that shows that substantively, the dog is yours.