I voted for "The Red Maw"! He was the greatest werewolf that had ever lived.
Bred from the foul breed of Draugluin, the first werewolf, and fed with Elvish and human flesh by Morgoth, Carcharoth was set as a guard on the gates of Angband. I never was into spiders and the Balrogs are cool, but there are so many of them... and they are not THAT special.
I probably vote for Carcharoth because i'm such a big fan of the Beren and Lúthien tale! My favourite animal in the books is by the way Huan!
Here is some more info on Drauglin:
He became involved with the Quest for the Silmaril when Beren and Lúthien had to pass him on their way in. Lúthien enchanted him with her magic, but on their way out Carcharoth attacked before Lúthien could enthrall him again. Beren held out the captured Silmaril in an attempt to stay the beast, but Carcharoth bit off Beren's hand and swallowed it together with the Silmaril.
The Silmaril burnt away Carcharoth's insides, and he became crazed with pain. A terror to Elves, Men and Orcs alike, he passed south through Beleriand, until he arrived in Doriath. There Beren Erchamion, Elu Thingol, Beleg Cúthalion and Mablung joined with Huan the Hound to Hunt the Wolf.
Carcharoth was killed by Huan, but Huan died soon afterwards from his wounds. When Mablung cut open the belly of Carcharoth, he found there the Silmaril with Beren's hand still around it, but when he touched the flesh it was swept away by a wind.