I have duplicates of some pets, but I have a method behind my madness.
Generally I avoid duplicates whenever possible so as to stay far away from the limit, as others have stated.
Whenever possible I try to find another pet in the same family with the same abilities, rather than get two of the same pet. For instance,there are 10 frogs that have the same abilities. Rather than get multiple breeds of the same frog, I have my Yellow-Bellied Bullfrog in P/P for power hits, and my Leopard Tree Frog in S/S for when I need speed. I can technically get ten different breeds of frog without ever having to get duplicates, simply by making sure I get a different breed for each frog type.
That's basically what I do with all pets whenever possible. Get a S/S Silver Dragonhawk for speed, a P/S Red Dragonhawk for power, and a H/H Blue Dragonhawk for health. The other Dragonhawks, do whatever you want; but you only need one of each. I bought a P/P Netherspace Abyssal, and got a H/H Minfernal—they're basically the same pet, but the Minfernal doesn't come in P/P. For cats you will never need more than a Feline Familiar, a P/P Cornish Rex, and a P/S Cat, and either a S/S Siamese Cat, or S/S Cheetah Cub for speed. All that without getting any doubles.
Exceptions to this are my power players for the tournament. I have about 30 pets that are doubles so I won't run out of my best players should one die or it's health is too low for the next battle.
Cageable pets, I leave them out of my journal and put them in a guild bank, where I will either give them to friends, or later level to 25 to sell on AH to lazy people for exorbitant amounts of gold—though I only give the best breeds to friends, so you know what I'm selling on AH. ;^)
. . .And if it's not rare, I don't care.
(True Story: I was leveling by the Dragonbone Hatchlings in Dragonblight, Northerend, and came across a P/P Dragonbone. Another player, obviously a collector, was standing there, seemingly AFK. But I decided to whisper her that I had found a rare P/P (I didn't need it as I already had one). She responds back "Thank you, but my invintory is already full." To add to this, she hadn't a clue about breeds, and had multiples of many pets, not even knowing what she had. For all she knows she could have three of the same breed, or even three of one pet that only comes in one breed. Well, she missed out because she had too many pets.
You could say she is a die-hard pet collector. But the way I see it, there are smart collectors, and there are. . .