One of the first things that really hit home with me when playing my hunter for the first time was when she dinged level 10 and was able to tame a pet. I basically tamed the first thing I ran in to on the plains of Mulgor. Soon after that I ran in to a cat with spots in the Barrens and was more or less awestruck by this fabulous spotted creature. I changed my pet and and stuck with this new cat for a long time.
These days I’m a bit more picky when it comes to my pets. Most times when I play solo I use a bear as a tank pet but when I join a group I have a bunch of different pets to choose from depending on the group composition. A group with no mage or shaman, no problem. I’ll bring out my core hound and pop Ancient Hysteria at the boss. Want some extra mastery? I’ll get out my cat. Some more crit? I have a wolf for that!
Pets used to be a bit like a cool looking DoT that could hold agro when needed. These days they add quite a lot of utility in group play and there are a lot of different options. If you’re curious on what pets gives what buffs/debuff I recommend you take a look the Warcraft Hunter Unions guide.
My stables are far from full and I enjoy to go on the hunt for new pets now and then. I don’t care if they are rare or not, but I do care about the function of them and somewhat of their color/design. My most recent tamed pet is a spirit beast (Ghost Crawler) for my night elf hunter. And I’m really looking forward to getting her a Quilen Pet as soon as I can.