I made up so many nicknames for most of them..it's sad.

I call Sesshoumaru (Something like that) for Fluffy ^^

If "Inu-kun" for InuYasha and "Sesshy-sama" count as nicknames then yes XD

I'll call Sesshomaru Sesshy sometimes.
Inuyasha I'll call Boy, or Idiot
Kagome, I'll call The Brat, among other unpleasant things
Miroku I'll call The Monk
Sango, is just Sango
Shippo is The Little Fox
Naraku I'll call Asshole
Hakudoshi is also The Little Brat
Rin is the Little Cutie
Jaken I'll call Little Toad
Byakuya I'll call The Kagura-wanna-be
Kanna the Ghost Girl
Totosai I'll call the Old Geezer
Kaede is Grandma
Sota is Turp
Kagome's friends are Girl 1, Girl 2 and Girl 3
Moriomaru I'll just call WTF (converted into a noun! xD)
Kouga I call Mister Hyper
Hojo is The Hopeless Idiot
Myoga I will call Squash that damn thing already! (YES also converted into a noun!)

See a pattern here, yes this is my exceptionally creative list read it and weep XD

@sesshyswind I love your list especially Naraku the asshole and Kagome the brat.^^

I'll jot more down as they come to me ;)

Lmfao @ Byakura the Kagura wannabe, Girl 1,2,3 and Moriomaru the WTF.

I call Sesshoumaru Sess, Sessh, or Sesshy (rarely). I'd never call him fluffy... o.0 though I have used that for internet usernames. =p

As for the other characters, I don't have nicknames for them.

Inuyasha: Jerk, half-breed, muttface, flea-bag, leg-humper, wet-nose, the walking fire hydrant, two-timer...other bad things.
Kagome: Girl who wears a skirt
Kikyo: Snow White (because she's so pale)
Sesshomaru: Sess, Sesshy, Fluffy, Lord Poofykinz,...that kinda stuff
Koga: Wolf-boy, cutie-pie, My little wolf pup...(I have others but can't think of any)
Sango: Boomerang chick and monk-slapper
Miroku: The walking vacuum cleaner
Shippo: Annoying twerp
Hakusoshi: Pink-haired troublemaker
Jaken: The follower
Totosai: I can't come up with anything better than Sesshywond's nickname

I called takemaru take-kun or sweetie pie or awesome guy because I love him