I like skins that change the champ as a whole.
Like, skins that change the champs apparence and gives their abilities different looks and sometimes even different taunts, VO's and such. It makes them feel....like a totally different person, while remaining the same? If that makes sense? It gives them a totally different feel. Like take all of Syndra's skins for example. Syndra is a magical dark champion who has a sort of powerful, mystic presense. Her Justicar skin pretty much transforms her into a light-wielding heroic, while still leaving that sort of mystery. Hr Atlantean skin pretty much totally transforms her into an aquatic sea-being and overhauling her abilities with water. It's just really cool to be able to play different variations of champs.