So. Many. Pets.

Available Pets
World Drop - 122
Quest Reward - 30
Vendor Purchase - 100
Profession Made - 51
Wild Pets - 303
Achievement - 30 (Stormcrow removed from this #)
World Event - 39
Promotion - 1
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TOTAL = 676 obtainable pets available to everyone without spending a single penny.

Pets Excluded from Count Above
Quest Reward - 1 ( [item=111660] )
Vendor - 2 ( [npc=65313], [npc=71159] )
Promotion - 29 (All CE pets *Starcraft, Diablo, WoW*, All Blizzcon pets, All RAF Pets, All Anniversary pets, etc.)
TCG - 15 (All)
Blizz Store - 15 (All)
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Edit: fixed links

A word of warning to all would be collectors out there.

I have over 600 unique pets, and was collecting three of each when possible and easy to do. I noticed when I got to 1002 total pets, I couldn't learn any new pets. I kept getting an error. I opened a ticket and spoke with a few GMs about this and they said the total number of pets is currently suppose to cap at 1,000.

I took every non combative pet like the Balloons down to one each, and took most of the cage-able pets from three down to two each.

So while you can collect enough to get this achievement, you can not collect three of everything in the game because it will currently to allow you to do so.

Stormwing is the true 600 pets reward
[npc=87705]