I stand to be corrected on this, but when I first played, the stats for pets were 1:1, that is if you trained any creature to 125 Strength, it would have 125 hit points, unless designed to have more. At some point, so the rumours I've heard claim, this was changed for small pets, so they had a smaller stat cap... however I've got a very old and very new cow in the stables, and they do seem to be training up to be very similar, so as I say I'm not sure if that's true or not. I do know however that I also have a 4x GM chicken (normal, not Battle or Greater) and rabbit with 125, 125, 120 stats!
However, what absolutely
was true is the "Leaping About Pets"; when the game first went live, the spell list that casting pets could use included Teleport, and Dragons were especially famous for using it constantly, often to the frustration of it's owner when it got stuck somewhere useless! There were urban myths for months and years after the cast list was changed that some pets still had that ability, especially when net connections were much worse back then, so you'd see characters juddering all over due to lag. I think they also had Invisibility for a while after Teleport, which could also have seemed like they were "leaping" about. But from what I understand, it's simply not possible for anything that casts to you use either spell now, no matter when it was born, as neither is on the list...
As for genuinely rare pets, I've only ever seen one definite one; a solid purple hued Greater Dragon, which was sold on Chesapeake about a year ago.
http://vboards.stratics.com/uhall/225550-rare-dragon-colours-now-bug.html
I also believe Ancient Wyrm's were tamable for about a day, and then stabled to hide them from the deleting fingers of the GMs. I do not know if any still exist, but they are unlikely to be shown off if they do, in case they get reported. Which is a shame, because they are the only truly beautiful pet in the Enhanced Client...