rarest pets are holiday pets and one-time-only event type pets, like storm beetle. the storm beetle was givien for the first million users who enrolled into ravenwood. It was available for "Play in November, Pet in Decmber" event, too.
To me a "rare" pet is only one that is retired. All the others can easily be hatched for to obtain. Pets such as the Pioneer Dragon, Danger Hound, and others which are retired are the ones that I consider as "rare." A pet that can be hatched for but is still often considered "rare" I believe is the Crimson Spectre obtained in through Pet Derby Tickets. Not many people have this as a pet. But besides that, there are not many others which are unretired yet considered "rare." I would definitely consider trying to get the spectre for your collection though!