You'll get a shorter list if you ask which ones don't.
Malzahar only has recolors.
Akali has 2 recolors and soccer skin.
Fiddlesticks has 2 recolors and bandito skin.
Cho'Gath has a recolor and Gentlemen skin.
Gangplank has a recolor and Minutemen (Sailor hasn't been released yet iirc).
Kassadin has 2 recolors and the Pre-Void.
Shen only has recolors.
Soraka has a recolor and the Divine.
Udyr has a recolor and Primal Skin.
Alistar has 2 recolors and the matador.
Kayle has 2 recolors and the Unmasked skin.
Mordekaiser has 2 recolors and the pentakill skin.
Kennen has 2 recolors and the Karate skin.
Malphite has a recolor and the Coral Reef Skin.
Garen has 2 recolors and the Commando Skin.
Olaf has 2 recolors and the Brolaf skin.
Taric only has recolors.
Thats it I think.
PS: Theres others I'm skeptical about but some might not call them just recolors.
Such as: Nasus's Galatic Skin, All of nidalee's skins, the Frosted Ezreal Skin. Just up to the user.
© 2013 Riot Games, Inc. All rights reserved. Riot Games, League of Legends and PvP.net are trademarks, services marks, or registered trademarks of Riot Games, Inc.