Shaco has obvious similarities to The Joker of the Batman franchise, such as his mysterious origins, his appearance (his face is often drawn with a long, sharp nose and a big smile, and they both have white skin), his voice, and some of his quotes which references Joker-esque quotes throughout the Batman franchise.
His story's description of him as "Valoran's first fully functioning homicidal comic" is a direct reference to Tim Burtons's Batman where Joker describes himself as "the worlds first fully-functioning homicidal artist".
Shaco is one of a few champions to actually have multiple textures in one skin. When he uses Hallucinate, his clone is a different color than that of the real Shaco, although this can only be seen by Shaco and his allies. To the opposing team, the two Shacos look exactly the same, unless you have some sort of external buff or item effect active.
Shaco's dance is The Worm. A side-by-side comparison can be seen here .
Shaco was one of the champions chosen for the Noxian pool available during the Ionia vs. Noxus match. However, he was not one of the selected champions.
Shaco once stabbed Ram Steed almost to death after Ram Steed interviewed him.
His name probably comes from "shako", which is the cilindric hat the light infantry used to wear in the 18th century and later; Shaco wears a cilindric hat in some of his skins as well. Assuming it is, the letter C may have been subbed to create an anagram of the word "Chaos" for creative effect.
It is also a possible reference to the Harlequin Crest, a Diablo 2 Unique item. The unique's base item is the "Shako".
This reference is further supported by the League of Legends post announcing the skins release, which states 'Go ahead and wind him up, if you dare.' as the first mechanical toys ran on clockwork mechanisms instead of batteries.
In his Classic skin's artwork, the spike on Shaco's right shoulder pad is visible, but on his in-game model it is not.