Atalanta is of course my personal preference, but since there's almost always a shaman, warrior, or death knight present, she doesn't usually get to run....unless all buffs are covered, which they often are, which makes her my first choice when I get a choice.
Hector comes next on the list, though the crit buff is usually covered as well. When Atalanta isn't with me, it's Hector who's my top choice of pet to bring when all buffs are covered.
Cassandra surprisingly moved her way up the list of pets-I'm-likely-to-bring, even though her buff also tends to be covered at this point. Because the physical damage debuff tended to be the one missing in early Cata, I got used to Cassie being with me, and now I can't imagine life without her.
Kallisto, who I now keep mentally confusing with Praline because they're both purple again (sigh), is up next, even though the bleed debuff is almost always covered. I shall have to make a point of bringing her if all buffs are covered, since it would be a very good idea to get to know her again.
Andromeda tends to fall next on the list, since I like buffing the casters if all the physical buffs and debuffs are covered. Besides, she's pretty! I never tire of seeing her, despite not being a huge dragonhawk fan in general.
Psyche isn't a pet I often find the excuse to bring, since sunders are almost always covered, but when it comes to min-maxing, it can be missing at times....which is how Psyche found herself as the first pet I had out in Firelands! Very cool.
Castor and Pollux are my utility pets who don't often get to tag along, but are happily welcomed when they do. Castor interrupts, usually in five mans, and Pollux brings a casting debuff that's helpful in a pinch.
Out of the PvP pet overlaps, Orpheus has actually gotten to tag along before, though Arachne could easily have subbed in as well; both have PvE specs with my PvE spec and if all buffs are covered, they're the same as other cunning pets - and they bring a snare. Tantalus does the same as a ferocity pet. With Icarus back, if I ever need a disarm in a PvE situation, I'll be bringing him.
All of my tenacity pets have filled in as PvE offtanks at some point or other, but my top two standbys are of course Ursa and now Kharon.
Such a diverse stable, even ignoring the fact that I cleaned out my exotic pets.