Sesshomaru from Inuyahsa?

Can anyone tell me what that furry thing that's always around his shouldrs is?

i think its his tail. it would get in the way if it was on his back like koga's and so many more of the other demons. but i dont think anyone is really sure of what it is!

No one knows. It's been theorized that it is his tail, but it is not attached to anything. In an interview once, Takahashi-san once said that she drew it there originally as armour, but exaggerated it while doodling and liked how it looked.

It supposedly was fur from his father, but considering it's a part of him... hmm... good question. Since he's a dog demon, though, that may explain it. :)

someone told me that it is part of his shield but others say that it is for carrying rin and jacken

It is known as Mokomoko which can extend and be used as a weapon. It's not actually apart of him. Rumiko Takahashi said that it's a fancy decorations for his armor. She said she got a little carry away while drawing his character design.