Scarecrow: Not commonly a living being, but in one specific case, a scarecrow was brought to life.
Champions: Fiddlesticks, receives quite a bit of attention, mage
Rats: Common sewer rats brought to life by excess chemicals and necromancy. Not given resepect in Valoran
Champions: Twitch is the first representative of the Rat-People, Doesn't receive a ton of attention, Stealth/DPS.
Undead: Any being previously dead, reanimated (Likely by necromancy)
Champions: Sion, Karthus, Urgot (Also a cyborg) These three are all vastly different types.
Wolves: Naturally born wolves are non-sentient beings who roam forests
Champions: Warwick, previously a human, Warwick was transformed into a wolf to reflect his evil mind and soul. There are also small packs of natural-born wolves which act as neutral monsters.
Robots: A man-made race consisting of machinery and oil as opposed to flesh and Blood
Champions: Blitzcrank, receives a fair amount of attention, Urgot is often considered a robot or cyborg.
Manatees: A rather proud race, their whereabouts unkown
Champions: Urf (R.I.P.) Urf was to be the first champion from the race of manatees. Unfourtunately, he was killed by Warwick before he could be formally accepted into the League