If, I have not signed a non-compete agreement with my current employer of the past ten years, and get a new job 40 + miles away from my current employer, is there any legal action that can be taken against me? It is basically the same exact job, just with a competitor in another state.

Not without a non-compete agreement and, even if there was one, many are not enforceable, depending upon the state and the restrictions.

To add on to what Scottb has offered:
Many firms have "agreements" with competition to not "steal" each others workers. If such an agreement exists between your employer and the prospective employer, it's "possible" that your offer could be rescinded.

Since you've not signed a non-compete, I'm curious as to what makes you think you may have trouble when you give notice.