Im told unborn valkyr by google but i have no idea what’s actually rare.
The one i invested the most time in trying to get was the vengeful chicken. Watched for those dailies for a long time.
Little fawn is all i need
Little fawn is all i have
Little fawn is what i like
Little fawn is what i love
Little fawn is what i care about
Little fawn is my only dear
Little fawn is my favorite
Little fawn 
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I have no idea which pets are rare these days but my favorite pet is Mr. Pinchy because I fished my butt off in BC to get him.
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prolly on my belly while doing a circular motion on my head with the other hand. Some people have a hard time with that. lol noobs
Gummi and Faithful Dog. Fave is Mr. Bigglesworth.
Still my favorite! A lot more people might have him after that, but I’ll always remember when I got him. My partner still played WoW back when the Baby Blizzard Bear was originally released in the game, and that pet reminds of of the fun times we both had adventuring through Azeroth. 
According to the stats on that website, Waxwick is my rarest pet (<1%). It’s the one you get for catching all the Khaz Algar pets. A lot of Khaz Algar wild pets are also showing that less than 1% of players have them. The rarest one I have from something besides TWW is Lady Feathersworth at 2%.
Hmm… Using the site above, most of the Khaz Algar pets that I have show at less than 1% obtained. As most rare, I’ll go with Deathy and Grunty though. Both Blizzcon pets.
Favorites… I have four dino babies named Little Foot, Cera, Petrie, and Ducky. Unfortunately, there is no stegosaurus battle pet so Spike is missing.
Got Hatespark the Tiny on my first run, I own both mirrors, but my favorite is the Dragonkite because I can Ai-Li mirror you, and then fly you forever. Add some biscuits and the Forgotten Feather.
Ai-Li’s mirror someone using Sandstone Drake, then use Narcissa’s Mirror on your kite, feed it a cookie. You’ll have fun. Not see much though. xD
That’s a tough question, I have over 1700. I don’t think I have a personal favorite. I really like Arfus, Baa’l, Will of Remornia, and Jenafur. I don’t really know what the rarest would be since the new expansion always has the rarest pets at the start.
That being said, baring any pets earned in TWW, I would have to say either Brul, Violet Violence, or any of the “Family” battler achievement pets
…oh, apparently its my Gryphon Hatchling. Looks exactly like the one you can catch in the wild. Mine was a bday present from so long ago.
Next is Albino Buzzard. IIRC you get that from a sack of pet supplies. I’d sat an alt out by the npc so I could do the daily, daily lol. And Alarm-o-dog which is one of my favorites. Got him for running pet dungeons. Huh, I got a lot of 2% pets…
rarest? probably the pet from the SCII collectors edition, or frosty from wrath collectors.
The rarest item i own though?
uhhhhhh i have 2.
Big blizzard bear, but hands down probably the most rare item i have is.
This item was only available in the game for the first day, of the very first brewfest. As it was a reward for a quest that blizzard ended up having to disable because it was causing massive problems in the game. So basically there was about a 12 hour window that you could have gotten this item.
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The 
best pet is Sunflower
“Theres a zombie on your yard~” 
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i still think my favorite pet is the sunflower
“there are zombies on your law-awn”
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Probably not that rare, but The Baby Blizzard Bear from 2008. Also my favorite pet
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I have about 500 pets not really sure what i have lol … but i do have baby blizzard bear
I’m just the same. I don’t like the ones permanently stuck hovering as much.
I do like the Pandaren phoenixes though. They were the best of the birds back in the day.
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Assuming you mean Battle Pet? If so - I dont know what’s “rare”, and I dont care anymore because the game is garbage and I’m leaving. I’ve been a big fan of battle pets since it came out, and I have 1,578 unique pets (per my add-on). You’re welcome to look at the collection. Enjoy!
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Vampiric Batling
Don’t make me choose.
Really wish i had mini diablo man. Biggest regret is not buying the collectors edition of vanilla.