Alrighty, congrats to everyone who found the pets so far!
Here's where they were hidden.
Azelf,
Uxie, and
Mesprit: Quote the first post of this thread.
Victini: The nickname for the Victini I adopted.
Latias and
Latios: Bottom of the rules.
Terrakion: My post explaining the format of the codes.
Virizion: The edit reason for the aforementioned post.
Cobalion: The edit reason for the first post of this thread.
Xerneas,
Yveltal, and
Zygarde: New FAQ entry.
Manaphy: My visitor messages.
Phione: Originally my visitor messages, moved to a new social group name.
Still available:
Zorua: This one is easy enough to find. I won't give you any hints because it's not rare and won't be removed for a while.
Keldeo: Act like a computer nerd.
I'll add some new codes soon.
You don't think I'd try that twice, would you?