A rare pet defines a pet that has a rare or unique skin (appearance). In this case, rare or unique means the skin is only possessed by one or a very few difficult to find or acquire mobs.
Since pet stats have been normalized, every pet of a particular type (i.e. cat, boar, bear, etc.) will have exactly the same movement speed, health, and attack speed. Primarily pets of one type are all the same as far as stats go. Pets learns new ranks of abilities as they go up in level. For more pet details and information on taming pets, see Pet (Hunter).
Though some of these pets are difficult to acquire, some hunters consider having a unique or especially good looking pet to be a big part of their enjoyment of the class, and go out of their way to get the perfect one.
Description: Two headed, white with black bands on its wings and body
Note: There are rumors that this mob is immune to frost traps.
Another very popular pet, there are several extremely rare and striking skins for cats. The white lions are very rare pets for Alliance players to get, since one can only be spawned by a Horde quest, and the other, while also a quest spawn, must be done at Level 60+ for taming purposes.
If you want something really rare and unique, tame Nuramoc. He has unique skins, really long respawn timer, respawns in different places, is level 70 and requires [Exotic Beasts] to tame. You can be pretty sure that you're one of few who have this pet.
Description:Bright orange with fainter yellow stripes
There are quite a few distinct raptor skins, though most can be found on typical mobs. Outland raptors have quite a sinister appearance. They are fairly easy to get once you reach the zone they are in, so they haven't been included here.
Ravager skins are widely varied, seldom with more than one mob for a particular skin. However, there are as of yet no rare spawns or particularly difficult to find ravagers, so each is about equally "rare".
There are currently no unique or rare scorpid pets available.
Serpent mobs are fairly rare. Most only appear in instances, and are elite. There is only one type of "normal" serpent, found in Shadowmoon Valley in Outland.
Description: Blue with purple stripes and black spikes
The wind serpent's few skins that are common are in reality quite rare, since only a few rare spawns have normal pet stats. When looking for a wind serpent pet, check the Wailing Caverns.
It's also worth noting Arikara here. While not a rare skin (it uses the easily accessible red wind serpent skin), it does have a special effect associated with it that remains after taming—whenever the hunter calls the pet, dismounts, or zones in, Arikara will arrive with the same puff of smoke and rumble that occurred when he was summoned during the quest.