Babies are occasionally born with fleshy growths, giving the appearance of a tail. The 'National Geographic' show I watched about it said it happens way more often than people assume (a lot of people seem to think it's some 3rd-world thing?) and the doctors just cut it off before they give the baby to the mother. I don't remember much more about it than that, and that the tails served no purpose whatsoever.
In the womb, we go through period of having gills, fur-like stuff, and tails (like a tadpole!), and my guess is that sometimes the tail-cells don't get absorbed into the forming baby and make their own thing.
Obviously, I'm no scientist and I guess you are looking for more magick-related stuff...
What use would a tail be? We are bipedal, and our centers of balance are pretty good. We have prehensile thumbs and our joints allow a pretty good range of motion. Just watch Cirque du Soleil.
Why do you want a tail? And what would you wear? You'd also need a strong sense of self, as you'd be setting yourself up for a lot of harassment.
In short: No, it is not possible to grow a tail because you are already fully developed. Your cells are already specialized and your human DNA doesn't really code for a tail.