Looks like some of us need to hit Snopes.com!
Shakespeare may or may not have invented the word 'assassinate' (and 'bump'), but 'assassin' is generally thought to come from the Crusades, where a group of Muslim fighters fought under the influence of hashish. They were called the 'hashashin', which mutated into the modern 'assassin'.
I've never found any good evidence suggesting that Shakespeare invented it, but it's commonly thought that he invented 'assassinate'. Maybe he invented 'assassinate', but not 'assassin'. Maybe the truth about that is for someone else to post