I like the nickname "Moony". It's nothing special, but it sounds so nicely and it really suits Lupin, not just because of him being wereworlf and being influenced by moon.
As for Won-Won, I laughed a lot at that one!
And Half-Blood Prince is such a strange nickname, isn't it? You see, it's Snape, a (former?) Death Eater who is supposed to value "pure blood" and yet he calls himself "half blood". I was thinking that maybe the Prince family was referring to him like that... (if they ever talked about him).
Oh, and Padfoot is nice too.