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’?