Rows 1 and 2 are my super-ultra-favorite pets right now.
Row 1: Tetsusaiga, Apollyon, Shikon, Naphtali, Vulkoor, Lannister, Reaper
Row 2:: Grimjaw, Leggo, Sounga, Dirge, Nemo, Dozer, Strawberry
Rows 3-6 are pets that I like but don't use very often. I've tried to release some but couldn't bring myself to pull the trigger, so they stay and collect dust.
Row 3: Poobah, Sheldon, Xaphan, Kybele, Celeborn
(to be re-named Tenseiga), Piandao, Skaza
Row 4: Rhytil, Ysuran, Rimebane, Shags, Phoenix, Oscar, Khamen
Row 5: Abaddon, Trixie, Beauty, Martin, Ransom, Shiranui, Rainey
(to perhaps be re-named Porkchop)
Row 6: Kip
Rows 7 and 8 are a mix of re-tames and things that I'd like to try, hence the duplicate families in some cases: Surge
(re-tame), couple of wolves I'd like to try, neat basilisk
(fave color from pics, might change mind after seeing in person), some boars because I feel like I need at least one, one of them there newfangled kitties that might replace Sounga, and a mana serpent to replace one of those long coiled ones that I used to have.
After all of this, I still have 10 empty slots, so I still have space for those tames that you don't expect but happen to stumble upon.
And unlike many of you (with such pretty stables!), my stables are utterly themeless. My favorite color's green, but even then I have a ton of non-green pets. Even my pets' names are whatever happen to pop into my head. Sometimes they're serious, sometimes they're silly. Maybe one of these days I'll make an alt hunter with themed pets, but not Rhyela.
Edited: Egad! I forgot one of my favorite pets! Fixed!