"Many beasts are now properly able to be tamed." - Recent Hotfixes.

[Aleksej89]

Does anyone know which beasts is blizzard referring to?
Are there any new (or old but unavailable) pet skins?

Too bad blizz does not like giving details

[BurningSkies2018]

I can only hope I can start taming beavers. I haven't tried since I saw it, however.

[Tannon]

That would be these pets below.... no new skins, but a lot that were classified beasts but still marked untamable.

Older stuff:

Shady Nook Guardian, Ashenvale
Imported Mottled Boar, Azshara
Dragon Turtle, Black Temple (thanks Spiritbinder!)
Halycon, Blackrock Spire
Mother Smolderweb, Blackrock Spire
Gizrul the Slavener, Blackrock Spire
Rockfang, Borean Tundra
Famished Bonepaw, Desolace (Spawns during quest "Early Adoption")
Snapjaw Basilisk, Desolace (Spawns during quest "Early Adoption")
Mature Swine, Durotar
Wild Mature Swine, Durotar
Wayward Plainstrider, Durotar
Duskwing, Eastern Plaguelands
Wild Sparrowhawk, Nagrand (Very difficult to tame as it drops aggro and flees. One way to maintain threat is to use Scare Beast on it and attempt to tame it while it's feared)
Fez, Northern Barrens (Ridden by Tortusk)
Jungle Serpent, Northern Stranglethorn, (Phased. Only encountered during the level 85 Zandalari quest chain in 4.1, started by Bwemba)
Deathclasp, Silithus
Savannah Boar, Southern Barrens
Queen Silith, Stonetalon Mountains
Razorthorn Ravager, Terokkar Forest
Naphthal'ar, Terokkar Forest
Rimepelt, Winterspring
Halycon, Blackrock Spire (thanks "evil950510"!)
Mothran, quest mob, V4W (thanks Caelan!)
Vampiric Shadowbat (Kara)
Hyakiss the Lurker (Kara) (note this one also has the wrong skin colour in Petopia. It will be corrected. It's minespiderskinolive)
Shadikith the Glider (Kara) - random basement boss in Kara
Crystal Fang (rare, BRS) - spawns by the last pack of spiders in Skitterweb Tunnels

And in Pandaria:

Needleback Porcupine, DW (thanks Spiritbinder)
Zan'thik Amberhusk, DW (thanks Spiritbinder)
Waste Scavenger, DW (thanks Spiritbinder)
Amber-fed Hatchling, DW (thanks Spiritbinder)
Young Stalker (spawn during fight with Rakira in JF) (thanks Spiritbinder)
Bookworm (Jade Temple quest phase, those green grubs you squish) (thanks Rarehunter1)

Information care of Wain from Petopian forums ~