In the absence of a prenuptial agreement, there are steps you can take during your marriage to protect your finances. If you receive an inheritance during your marriage, do not commingle that money with any marital property or accounts! Meaning, set up and keep a separate account, titled in your name alone, for the money received from an inheritance.
The same holds true for premarital assets. For example, lets say you own your own home then marry and you and your spouse live together in that home during the marriage. The home is your premarital asset, so long as your spouse has not made contributions to the property, i.e., assisted in payment of the mortgage during the marriage, used marital money earned during the marriage by both of you to make improvements on the home or pay the taxes. Although the laws vary from state to state, generally speaking, if this occurs, there is going to be some claim against the property by your spouse at the time of a divorce.
Visit EqualityInMarriage.org for more information on postnuptial agreements, what they are, what they can and cannot do and how to go about presenting a postnuptial agreement to your spouse.