I am not a lawyer, nor have I ever been a lawyer, but I have heard of several cases.
In California it had been the law that if a man is married to the woman having the child he is the presumed father and is responsible for the support of the child, even if it is later proved that he is not the biological father. That has been challenged, I believe, but I think it is still the law.
Conversely, there was a man who impregnated a girlfriend who while legally married, was separated from her husband. She eventually returned to her husband and told the inseminater to pound salt (or perhaps something else...how crude of me!) when he wanted visitation with the child. She was upheld in court; if the ruling held on appeal, I do not know.
As related in some posting(s) above, in many jurisdictions if a man admits to paternity and is later proved not...he is still on the hook as if he were the daddy, the reasoning being that it is in the best interest of the child to have his financial and physical (one hopes) support as the 'father'. It also saves the taxpayer from supporting the child.
I'm sure there are other permutations of this problem. DNA, the evolving concept of marriage and family, and men's rights orgs. murky up the situation.