It's my understanding that a proper birth certificate from any country with which the US has diplomatic relations will be recognized for identification purposes.
As far as I know, the same applies to mariages: if you got married in Kenya, the US will recognize your marriage when you're visiting, and each spouse will be allowed access to the other in a hospital, for example.
This becomes a bit muddy when we're dealing with two men or two women who were married in a country that recognizes marriages between partners of the same sex (for example, Canada). Many areas of the US will probably try not to recognize the marriage of a gay couple that got married in Canada if the issue ever comes up. I'll be curious to see how that will pan out in court if there's ever a dispute over it.
But as long as you're married to someone of the opposite sex, you should have no problems.