I've personally always been a Ranger at heart. I surround myself with animals IRL, I love to work with them (hunting, working dog training and hopefully one day work as a security guard with my dog by my side) and I love the idea of a human being that can survive in nature without difficulty, without even carrying anything but tools that she can carry herself.
For me, the obvious choice in WoW, was the Hunter. So far I've had a lot of fun with it (except for guns and x-bows..I want JUST bows!) and I've found and tamed each of the rare (unique) beasts available in-game. I feel a connection to them due to the work I put in, but...you can't say that the pets are exactly your companions, they're just there!
What I hope to get from a GW2 Ranger, is the following:
Bird pets that actually sit on your shoulder, that fly and can be sent on foes. No WoW style huge birds that never land but just flap alongside you for eternity, and are too big to sit on your shoulder/staff/whatever. And also that HORRIBLE flying close to the ground, never taking air.....they're basically deformed eartbound creatures once you tame them.
Personality. Yes, personality. This does not mean something complicated, just simple things such as the pet exploring, sleeping when you stand still, sitting down, your character stroking its head or giving it a pat once in a while. Maybe some sort of mechanic that rewards you for not switching pets over and over just to keep different looks, much like the very simple mechanic of a horse that you steal/take/tame in Red Dead Redemption gaining trust in you, and thus gaining the maximum stamina. John Marston (the character) also pats his horse when sitting on it in a very nice way that gives me as an animal lover a bit of fun.
Actual protective stance. By this I mean that the pet will react to the surroundings, if it hears and sees a foe going for you, it will intercept/warn or at least try to do so even if you've put it on passive..it should still be aware, even if not taking action. When training working/protection dogs, you teach the dog to react with defense if someone acts hostile to its leader, even if the leader does not give a command. A dog will often know by nature, without training, if the human is in danger even long before the human knows it herself. I find it hard to believe that the pets used by characters in games such as these that we play, would wait for the foe to strike their master...they're trained and battle-hardened, they should show SOME ferocity when the situation calls for it.
Emotional displays. Animals involved in a fight growling and showing they're there, they're aware and they're ready. In short, give the beasts some expressions as well. This could also come in handy for stealthy reasons since the Thief could see if they're about to trigger the pets awareness...the ears could go back, slight growl, sniffing/looking around etc.
The pets should be a danger to other players. Being chased by the rangers pet, should be something to consider for the other player. In WoW Beastmastery we've been given a bit of that since the pet deals major damage with Kill Command, but in the other specs, people can even play around with the pet chasing them....
In short: I want the Ranger class to really feel like a ranger, and the pets to feel like reliable companions that give you more in return than just standing around looking like statues with a pulse.
What do YOU want from the pets?
(And going all "I'd not want pets at all, gief gunslinger!!" is not what I'm asking for here, if you don't want pets, play Engineer or thief).