Generic shooter + ??? = Great

It is commonly known that most all First person shooters now a days are all mashed together in a cluster of unoriginality. But what makes an average shooter a great one, maybe even a classic? There are a few things that come to my mind when I think of this question such as Story, Setting, Over the top-ness, or just great weaponry.

But for you what does it take for a great and memorable shooter to be made, and what FPS's have done it right.