On the American side again: of the amphibian species Jay listed, my experience is that Panamanian golden frogs are quite common; the rest I'm not sure about, although my guess is that Wyoming and Houston toads are only kept in a small number of places.
Some exotic species that I have seen frequently listed are:
- Surinam Toad
- Tomato Frog
- Vietnamese Mossy Frog
- Cane Toad
- Kaiser's newt (endangered)
- Anderson's newt
- Aquatic caecilian
- Mandarin newt
- Both species that vogelcommando named
- Axolotls as Zygodactyl mentioned
And then also tree frogs and PDFs.