My favourite non traditional pet would have to be rats. I love them. They are sweet, loving, and clean animals, unlike what most people think. I've had many over the years, including a hairless rat I named Saggy. I had her for about 5 years before she got cancer then died. Another rat I had that I tried to breed, was about 8 pounds, and more than a foot long not including his tail. Boots always seemed to squish pontential mating partners. That was until my sister accuired a huge female rat herself, and we bred Boots and Socks together. A little more than we meant to, but until Socks gave birth to 2 hairless rats that my sister let me have along with 2 other rats of my choice.
Rats are simply the best, I would recommend a rat as a non traditional pet. They are fun and loving, you must interact with them to be such, though.