Mourning Gecko (Picture from TheBioDude.com)
This tiny gecko is the basis of the main characters of Wizard Lizard Chronicles. While our protagonist is human-sized, these creatures are small enough to crawl on your thumb. They reproduce by parthenogenesis (mom lays egg, clone hatches), so they're almost entirely female.
Like other geckos, they can climb just about anything and don't blink. They can also detach and regrow their tails.