If I owned a house before I was married, and have no mortgage on it, is my spuse intitled to any of it if we get a divorce?

If you owned it before marriage and there was no increase in value of the property during the marriage that can be attributable to your spouse, then most likely she is not entitled to any part of the residence's equity.  You should consult an attorney.

I am not admitted in Kentucky.  Property bought prior to marriage is separate property.  However, if it used as the marital residence or you hold it out to be such, or if your spouse contributed to its increase in value, it (or a portion of it) can be considered marital property for purposes of distribution upon divorce.

A pre- or post- nuptial agreement will take care of any doubts.  Think about it.