2.0/TBC news. My main became a warrior, so my new tips are from that persepctive. Because I played a hunter for so long, there is nothing I love more as a tank than running with a hunter who knows how to trap and use his or her pet.
Pets are a big part of being a hunter, but they can cause major problems or even be useless in some instances.
The right pet can tank!
Don't have a tank? Don't have a druid? All your pallies off doing something else because they can actually kinda kill stuff? If you're with a good group in an instance that isn't TOO complex or out there, your pet can tank. I'd not recommend doing this with a PUG, but I've had my pet tank Blood furnace, a hunter in my alliance guild tanked one of the Coilfang instances with his kitty (Yeah, a cat), I've heard of owls tanking instances, too.
Pet = Fantastic offtank
As I tank now, I absolutely adore pets as offtanks. Especially seeing as I'm relatively insane and will do things like Shadow Lab without anything other than a hunter for CC (A winner is us!). While A well geared tank CAN tank like 5 things, if there's something that can offtank, like a pet, please use it! Ask your tank or leader to mark a target for the pet. Or use your pet to control the mob you're chain trapping around the instance.
If I assign a hunter to chaintrap a mob (BLUE SQUARE) that mob will be killed last. If I assign a pet offtank target (Moon) that mob is killed first if the pet is a 98 lb weaking who can't take hits, or second if the pet can tank, which gives me time to get a metric butt-ton of aggro on all the other mobs in the pull.
Fear and pets
Don't send your pet in after a mob that fears, especially in strathlome. Double especially if your pet has dash. Your pet will get feared, and if you are unlucky, it might bring the BILLIONS OF MOBS in Shattered Halls (Your tank will make a grrface) with it.
Runners and pets
In a similar tone, don't send your pet into rooms where there are close packs of runners. You can get mods that will put your pet on passive if it chases after a runner, but it's better to play safe and keep the pet at your side.
Passive, please
Keep your pet on passive when you're in an instance unless it is off tanking. Play it smart and be in control of your pet at ALL TIMES. Your pet can save a healer from certain death, or can add much needed DPS. If you switch your pet to aggressive for PvP or for any type of zerg situation, make sure the pet is on Passive before you start doing anything else.
Put your pet away
If the group leader asks you to put your pet away (Which doens't happen any moe in TBC. Huzzah! Pets for the win), put it away. If you are jumping down through shortcuts, put it away. Some people can pull off the eyes of the beast/jump off the cliff trick but most people can't (I know I suck at it), and you'll bring runners. It isn't pretty.
Pets and raids
This is where things get fun. I don't have much experience with TBC and pets in raids as I am now a big, dumb tank, so I don't know if this has changed at all.
Pets can be used to add DPS or for protecting squishies. If anyone can enlighten me on the usefulness of pets in places like Kara, Mag or Gruul, please let me know!