Where did the nickname for Nightcrawler come from. I get the elf part of the name, but fuzzy?

Yeah, I remember in the X-Men: Evolution cartoon, he couldn' t touch people, even in his holograph form, because they would feel the fur on his hands and skin.

Maybe the girls just think he feels fuzzy? :P

Its probably less literal, and more of a term of endearment.

he actually does have a thin layer of fur

wasnt that something Wolverine started? if thats the case their isnt any more logic
to it then the nicknames Hulk gives people. Wolverine calls himself " the ol' canucklehead "
 
also noted, were that Wolverine, who is he to call anyone else on 
hirsutism? lol, he has longer hair coming out of his arms (and it regenerates)
than most people have on their heads.

"he actually does have a thin layer of fur "

I don't think it's a term of endearment. I think he literally has a coat of fur all over. Captain Britain called him a furry goblin when he was mad at him.

In X-Caibur, Mystique mentioned his father passed down furry genes to Kurt.

Someone once petted him, saying it was like velvet.

His skin is actually white, however he has a small layer of fur that can absorb light.