I would have to say that the best "pet" that any of the parties I've DMed for ever acquired was a kobold named Spot. They originally rescued him from a group of goblins that were using him as a slave and a cook. The kobold was supposed to be a plot point that gave the characters some additional information and opened up some possibilities. However, instead of following up on any of that -- and indeed, instead of asking any questions and so ever LEARNING any of this -- the party basically said, "Hey, cool, someone to cook for us," and took Spot on.
Spot not only stayed with the party for the rest of the campaign, he saved their butts at one time from a TPK because the bad guys didn't notice him and Spot knew where the healing potions were.
I got some great roleplaying out of Spot. Like when the Cavalier character had to convince some noble buddies that Spot was part of his entourage, not a pest to be immediately killed. Then there was the time when Spot accidentally ended up with the pair of Gauntlets of Ogre Power from a dragon hoard. One of the other party members tried to talk him out of the gauntlets, but Spot's argument was that they were small enough for him and so wouldn't fit the character. (Back in the day when magic items would resize to fit you.) The player never thought of ORDERING Spot to give them up, he just kept wheedling.
The best part about Spot was that he was pretty much unkillable in the early parts of the campaign. He was a plot point, remember? He had been the familiar of a powerful human wizard who got tired of his familiars dying in magical accidents or from the splash of spells and so put a ton of magical protections on Spot. In modern terms, the kobold had a high natural armor and a high spell resistance, not to mention a bunch of hit points from his high level master. Spot had outlived his master, but still knew where their old lair had been.
Of course, none of that ever came up because the party used Spot to set up camp, cook, and clean, never bothering to actually TALK to him. (But who am I kidding? It was back in the days when nobody really talked to NPCs anyway.)