I have a FICO score of around 800. My Significant Other does not know her score, but her report shows several liens, unpaid cards, etc. Her Ex husband, while they were still married, decided he wouldn't pay taxes, credit cards or doctors (but he kept assuring her he paid them, even signing her name to checks & amended tax returns - that she did not know about. That is a totally different subject, of course) All of those obligations were Joint.
She is about to move in with me. We will not be getting married. Will her credit history ever have any effect on mine?
What can I do to assure it doesn't?

If you were to get married and lived in a state that recognizes married domestic partners, then I'm sure it could. But, even if you do not get married, the only way her credit could affect yours is if you were a co-signer of say a loan (car, mortgage, business, ect), or jointly ventured into credit cards or other debt obligations with her.