I'm sitting here trying to compose the company Mission Statement and I don't know which is correct: "state-of-the-art" or "state of the art".

Can anyone help me with this one?

Prsonally I would go without the hyphens as I think four hyphenated words is getting a bit ridiculous, but I'm sure other people would say the opposite. I don't think it will be too important which you select. Although it is a bit of a cliche now...
It depends on how you will use it.
The hyphenated one is used as an adjective before nouns
(as in "state-of-the-art technology). Many native speakers tend to
omit hyphens, which I believe is a bad habit.
If you want to use the term as a noun, do not use any hyphens.
Then it will be "the state of the art." Do not add an "s" to the word "state."

In most cases, hyphens are used to connect words and make them
work as adjectives before nouns.