I'm pretty sure if you can prove that the child is not yours, you don't have to pay.
It's kind of assumed that someone is the kid's male biological parent. And then there's things like this...
http://www.csmonitor.com/2007/0209/p01s01-usju.html
"Last week, the Florida justices ruled 7-0 against him. They said that Parker must continue to pay $1,200 a month in child support because he had missed the one-year postdivorce deadline for filing his lawsuit. His court-ordered payments would total more than $200,000 over 15 years to support another man's child."
http://www.totaldivorce.com/news/articles/children/time-magazine-duped-dads.aspx
"The Time article examined a case in Colorado in which now 36-year-old Dylan Davis learned after his 2000 divorce that he was not the biological father of his 6-year-old twins. Davis had to give up partial child custody of the twins as a result of the negative paternity test. State law still requires Davis to pay $663 a month in Colorado child support even though he has had no contact with the girls since his ex-wife moved to another state. Davis has lobbied to the Colorado legislature to change the statute so that he and other "duped fathers" won't be held financially accountable for children who are proven not theirs in paternity suits."
There's a lot of cases like that actually. It seems a lot of courts prefer to do what they think is best for the child even if that is not what justice dictates.