There was one campaign that featured a hawk that was particularly prone to snatching any gold coins or other small items made of gold and hiding it in whatever was most equivalent to its "nest" at the time, whether that was the birdcage in it's wizard's dorm room, or her traveling pack with a perch attached. It came up throughout the campaign as both a comic relief "as you count and separate the treasure, Drace starts collecting his share" and as an explanation for where anything small enough and appropriately shiny had ended up if the players couldn't remember where their characters had actually placed it (such as when they couldn't remember who it was that actually had the magic ring they found, and found it in Drace's cage, where he put up a fight to keep it and pouted at losing it for days, inconsolable even by stacks of coin - until there were enough that he could sit surrounded by them as if his entire nest was gold).
There was also an otter, the name of which I forget, that would constantly be darting this way and that, sniffing about frantically as if something tasty might be nearby, and yet always seemed to be chasing down gemstones rather than morsels of food - even if it meant pick-pocketing some character that had no expectation to be "burgled by some manner of weasel" (which is a quote that I can't remember the exact timing of, nor whether it was an NPC or a PC angrily shouting it as an explanation when asked "Why are you so upset?").
Then, there is the cat. I say "the cat" because the reality, unrealized by my players as of yet despite a decade of opportunities, is that it would be more accurate to say that this particular cat has been in the possession of eight wizard familiars (thus far) and visited many different worlds and times than to say that any one of those wizards had this cat as a familiar. His personality and appearance have remained constant, both serving as hints (as of yet un-taken by my players) to the fact of the constantly recurring cat. He is thin, grey, fond of wizards of advanced age because of their proclivity for absent-mindedness necessary for the cat to insinuate himself and be assumed their familiar despite them having not summoned up a familiar (even though that same absent-mindedness irritates him the moment it means that his presence has slipped their mind) , beer, and looks that suggest if the cat could speak it would say something sarcastic, condescending, or both.
Of course, the cat is my personal favorite. The cat's appearance and the manner I describe for the cat are those of a cat I lived with long ago, and I like to imagine that it is that very same cat having gone on to great adventures rather than death. I plan on actually pointing it out to the players, if they haven't caught on as of then, after the ninth time they have met the cat (with different PCs, and accompanied by a different wizard) that this one cat has been all of the cats that showed up accompanying wizards since they met me (twice as familiar to my PC wizard, and six times including our session just last night as companion to an NPC wizard).