Grin Like a Cheshire Cat: The pseudonymous British satirist Peter Pindar (John Wolcot) first used this expression for a broad smile in the late 18th century. 

But it was Lewis Carroll who popularized it in Alice's Adventures in Wonderland (1865), with the Cheshire Cat in his story, who gradually fades from Alice's views, while his grin the last part to vanish.
 
To grin like a Cheshire Cat probably goes back much further than Pindar, and the source could be Cheshire cheeses that were at one time molded in the form of a cat. Supposedly, the cat was grinning because the former palatine of Cheshire once had regal privileges in England, paying no taxes to the crown.
 
Another story relates the expression to the attempts of an ignorant sign painter to represent a lion rampant on the signs of many Cheshire inns (his lions supposedly looked more like grinning cats).
 
And one other story credits an eponymous forest warden of Cheshire named Caterling. In the reign of Richard III, it's said this Cheshire Caterling stamped out poaching, was responsible for over 100 poachers being hanged, and was present "grinning from ear to ear" at each of these executions. To grin like a Cheshire Catling became proverbial and was later shortened to grin like a Cheshire Cat.

**For some more fun facts about the history of Alice in Wonderland (and the making of the Tim Burton film), be sure to check out this post.