Rarest skins include: UFO corki, King Rammus, Black Alistair, Silver Kayle, Trophy Ryze, Human Ryze, Goth Annie, PAX Twisted Fate, Medieval Twitch, and other past limited edition/legacy skins. But, some of them are more "liked" then the others, like: Snow Bunny Nidalee, Kitty Cat Katarina, etc...
Edit: Just saying, I own UFO corki and king rammus. When I play ranked and others summoner's rift game, people often ask me how I got them, and how they can get them for themelf. Unfortunately, they are no longer available. BUT, Riot are working on a kind of "Auction House" for people to sell their skins for Riot Points. So even if skins are no longer available, it might become possible to get them in the (far) futur.
Last things, my favorite skins are : Special Force Gangplank, Mecha Kha'zix, Steel legion Lux, Firefox Ahri, Mistletoe Leblanc, Bewitching Nidalee
