An eye-opening 2005 paper estimated the number of children who are not the biological offspring of their presumed father.
Looking at studies from around the world, it concluded that the median number of kids who are not the children of the person they call ‘dad’ is 3.7% with studies typically finding a rate of between two and ten percent.
This is presumably due to children being conceived during clandestine affairs. Whether you think that 3.7% is a low or high figure depends on your view of how human relationships work in real life.
If you want more details there’s an excellent post on Gene Expression which discusses the evidence based and the ethical implications for these findings.
For example, if a child needs genetic testing for medical reasons what should the presenting parents get told about incidental discoveries of ‘paternity discrepancy’?
Link to 2005 study on ‘paternity discrepancy’.
Link to excellent Gene Expression post on the same.
Mind Hacks 
There’s more to it than “clandestine affairs”. Here in the US, at least, there are generations of young ppl who think of a marriage certificate as an “inconvenience”. Large numbers of couples don’t use birth control because it detracts from “the heat of the moment”, or it’s uncomfortable, or The Pill makes a woman sick, or what have you. Couples make a baby, break up, join another relationship, make another baby, break up, etc to the point that a woman’s six children might have five different fathers, or a man’s six children might have five different mothers. There’s nothing “clandestine” about it, nobody’s shy about changing partners as often as they change their socks.
May I suggest that you actually read the paper? Or better yet, may I suggest that you invest in some reading comprehension skills? These figures do not speak to the cases you described. They talk about cases where a father thinks that he is the biological father, but isn’t.
There’s something wrong with Khan’s math. How does 10% falsely attributed biological paternity mean “that nearly 30% of paternal grandfathers are not paternal grandfathers”? It’s 19%.
Re “Studies which rely on a data set consisting of men who have requested paternity tests are strongly sample biased toward those who have a reason to have suspicions”. Maybe. But maybe they are strongly sample biased toward those who care about biological offspring and are jealous of other men? And maybe these men and their partners aren’t the most promiscuous? Maybe the exact opposite from what he assumes is true. He presents no evidence for his assumption.
Chimera, or the “vanishing twin” giving a person two different sets of DNAs as well as the possibility of a different blood type for specific organs should also be taken into consideration when evaluating paternity/maternity by way of DNA testings – especially since most Chimerical cases were discovered by accident during organ transplant compatibility testings, it remains doubtful one would end up testing each and every organ in their body to check for any influence of a twin who didn’t make it next to the surviving body’s to reduce confusion with identifying biological parents.
With Chimera cases; naturally, the ones on the person’s Birth Certain are their biological parents ..technically, their twin sibling “gave birth” to them.
Chimera, or the “vanishing twin” giving a person two different sets of DNAs as well as the possibility of a different blood type for specific organs should also be taken into consideration when evaluating paternity/maternity by way of DNA testings – especially since most Chimerical cases were discovered by accident during organ transplant compatibility testings, it remains doubtful one would end up testing each and every organ in their body to check for any influence of a twin who didn’t make it next to the surviving body’s to reduce confusion with identifying biological parents.
With Chimera cases; naturally, the ones on the person’s Birth Cert are their biological parents ..technically, their twin sibling “gave birth” to them.
Please delete this post of mine as there was a minor typo and I somehow posted this twice!
Apologies in order,
Isz