At least our dogs do. I was thinking the other week about why this is the case, and actually, if you think about it from the dog's perspective, it actually makes a lot of sense that they would have a special animosity towards mail carriers. Consider:
You are a dog. You live in a pack with one or more humans, maybe some other dogs or even some cats. You have a very well-delineated home territory; in fact, you spend quite a bit of your time inside a closed structure that defines your home territory.
Almost every day, a particular man (yes, man, not woman: I am writing this from the perspective of my dogs, and our mail carrier is a man) comes on to your home territory, and approaches the enclosed structure which you are so keen to defend. He's a stranger; possibly an enemy, more likely a guest. Certainly someone worth greeting and smelling.
But this particular man, he doesn't come in to be smelled. Rather, he stops at the threshold, fools around with some random objects that seem to be interesting to the humans for some reason, and then turns and goes. Perhaps the stranger was an enemy after all, and you frightened him off?
But no, there he is, the very next day, back again. Once again he approaches, but stops just out of sniff-range, turns and goes.
What the hell is he playing at??? Is he scouting out a possible future attack on your pack? Does he have something to hide? Was he frightened by your display of dominance, and if so, why does he keep returning, day after day, almost every day?
You never quite solve the mystery of the mail carrier, but you know something isn't right. This is not normal behavior. This is not how you approach another pack's territory. You're not quite sure he's an enemy, but he's certainly not a friend. And one thing's for sure: There's no way you are going to let your guard down when this mysterious stranger is nearby. You can't shake the feeling he is up to no good, and you respond to his presence accordingly.
And if you manage to get outside when this shady character comes around, you might even pre-emptively bite him. It's the only responsible thing to do.