The archetypical shapeshifter was Zeus. Right? He was king of the gods, his wife was rightly jealous. He loved to swing, but was too glorious for an ordinary mortal woman to look upon and live.
So, he went looking for love in animal disguise (except for the time he turned himself into a shower of gold, which I hope represented coins... sovereigns, perhaps).
I guess the ancient Greeks didn't have a problem with bestiality. Nowadays, I think we prefer our dragons, bears, wolves, lions, horses, centaurs, elephant seals, very large bats... you name your beast! to shift into manly form in order to make love.
Occasionally, Zeus turned the woman into a cow --Io, if my memory serves-- so he could act the bull. In some cases, after he'd had his fun, he neglected to turn the woman back into herself again. This was for her own protection, the myth writer would say. Now, speaking personally, I don't think I'd want to live out my life as a bovine after a quickie with a shapeshifting god, even if my eternal reward was to have a distant star or planet (or moon) named after me!
We have swans on our lake, and they are fiercely sexy birds, so I can understand the fascination of Leda and the Swan (though I've never figured out why Leda had to lay eggs afterwards, and I've occasionally wondered how big a swan would have to be if it was really a godly hunk in disguise).