We have had this up a few times, and the answer always is, that its hard to say what breeds are the best, without bringing up a specific pet (and even then it can be).
Power is usualy the best, speed is obviously strong for moves that benefit from it, like interrupts, stuns and dodges. HP is usualy only good if you have a lot of stalling abilities. Balance is for when the other breeds arent good :P
But i can try bringing up a few things:
Link to family chart: http://cdn.warcraftpets.com/images/pet- ... .v8271.gif
Flying - you rarely need speed, since they have their speed buff, so power is usualy the way to go on these.
Humanoid - They heal based on their max HP, so they gain more out of it than others do. But unless they got some other stall ability (like the anub idol sandstorm), its not enough of a gain to be worth it. But a lot of them also have interrupt or stun abilities, that makes speed better.
Beasts - Their breed ability scales with power, with can make for some really strong hits. But its hard to say here, speed will make sure you can get some hits in when you are under 50%, and same with Health, since it gives you more health to probaly soak up an extra hit.
Magic - It doesnt benefic from anything specific, but health doesnt do much on them, since they cant take massive hits anyways, so low health magic pets can be very strong, since the hp stats roll over into speed and power.
Undead - Since they will always get up when killed, and get an extra turn, speed doesnt do much for them, you will always get the same number of hits in doing a fight. Tho you will take a hit you wouldnt if you kill a pet that goes before you, but with enough power you probaly also killed that pet a turn earlier, saving a hit either way.
Mechanic - These scale with health, since you get returned with 35% health, health is basicly 1/3 more effective. But as with humanoids, if you dont have some defensive abilities to support this, its not worth it.
Aquatic - They offen have healing abilities, and those scale with power, so a lot of power is the way to go. This doesnt count for % based healing, where you want as much health as you can instead.
Dragonkin - Scales with power, you can get in some insane hits the turn after you killed a pet. I find that this ability offen go to waste tho, because you end up bringing a pet to under 25% without killing them, and you next turn you would have killed them even without the buffs. Tho power is probaly still the best in general.
I cant really think of anything specific with Elementals and Critters :)EDIT: Just want to point out my views are for pve, i dont care much about pvp.
Also some of the "racials" have changed with the patch, it might change things.