I'm looking for pets that absolutely annihilate specific families, ie family X. Usually this results from fortuitous combinations of both being from a family that is resistant to X, and also having an attack that is strong vs X. For example, Jade Owl would be the ultimate anti-Aquatic in my opinion, because he's the only Magic pet with a Flying-type attack. Magical Pandaren Dragonling would be the ultimate anti-Magic pet for similar reasons. This combination doesn't always happen, though: for example, there is no Flying pet with a Mechanical attack, which would be the ultimate anti-Beast; therefore the ultimate anti-Beast is not so clear-cut.
The main use for this type of pet right now is to easily beat a Master Tamer with only 1-2 high level pets, so that the other slot(s) can be low level pets, which is my preferred method of leveling. I'm also thinking ahead to the Legendary pets that are coming in 5.1 or later, which presumably will require serious counter-comping to beat.
So here is my current list of ultimate anti-X pets: I'd love to get input about suitable alternatives, especially in the cases where there's no clear-cut choice.
anti-Aquatic: Jade Owl -- pretty obvious choice, but he only comes in Uncommon until we get battle stones, so the higher stats on a suitable rare could be preferable.
anti-Beast: Darkmoon Zeppelin -- there is no obvious winner here, but I chose Darkmoon Zeppelin because it has strong mechanical attacks while also having Decoy, which is very good against beasts who tend not to have multi-hit attacks (making Decoy prevent two full turns' worth of damage).
anti-Critter: Flayer Youngling -- a humanoid with beast attacks. In practice I also really like Magical Crawdad or a random Crab, as they have beast attacks along with a shield, which shuts down Stampede and Flurry.
anti-Dragonkin: Scourged Whelpling -- this is the only undead with a humanoid attack, but Call Darkness is on a long cooldown and is at odds with the Whelpling's Plagued Blood ability. Plagued Blood plus Tail Whip is pretty good though, and he does very well against dragons in practice. I usually save Call Darkness for the coup de grace, but it is also good against Healing Flame on Onyxian and Crimson Whelplings. Flayer Youngling is pretty darn good against dragons too.
anti-Elemental: Rapana Whelk or one of the other snails -- these are critters and have Dive, which has a long cooldown and high miss rate but is brutal when it lands. Shield and Absorb keep them alive pretty well too, especially when incoming damage is nerfed vs Elementals. There's plenty of room to find something better here though.
anti-Flying: Emerald Whelpling -- there are actually lots of dragons that have magic-type attacks: Lil Tarecgosa, Sprite Darter Hatchling, Azure Whelpling, Netherwhelp, Celestial Dragon. Emerald Whelpling is my favorite due to having both Moonfire and a spammable magic attack, plus heals. Sprite Darter Hatchling is probably the 2nd best, but there's multiple good choices here.
anti-Humanoid: I'd pick one of the various spiders, my favorite is Crystal Spider. Since Leech Life is an undead ability and is buffed by the target being webbed, it creates a huge life swing vs humanoids.
anti-Magic: Magical Pandaren Dragonling -- not much competition here, but he's only uncommon which is not ideal.
anti-Mechanical: any Elemental, really.
anti-Undead: any of the many many Frogs -- aquatic with 2 critter attacks, plus either a heal or Cleansing Rain. Cleansing Rain and the aquatic innate ability both reduce the amount of DoT damage taken, which is a big source of undead damage. As a runner-up, Summit Kid is still very good against undead too, even in his recently nerfed state.