What are the problems that overpopulation causes?

One of the issues that is caused by overpopulation is the shortage of resources. About one billion people worldwide lack a constant supply of clean water. Approximately 25,000 people die, roughly 18,000 of those being children below the age of five, due to malnutrition each year.
Another issue is conflict. People are more likely to be on edge with a larger population and less likely to have a friendly approach even to their neighbours. In the worst case, a conflict to lead to a full-on war or genocide. (Yes, genocide would technically reduce the population but it is not humane nor polite in the least, so that shouldn't be looked at as a solution.)

In the picture above, you can see that these villagers do not have a supply of clean water, nor is their village very clean. This could lead to numerous health problems.

Here is an example of pollution. As the population increases, the demand for certain things goes up and companies turn to factories to produce artificial resources in large amounts. Unfortunately, these factories are not and have not always been environment-friendly. Due to pollution/decrease of air quality, childhood asthma rates have increased.

http://peakoil.com/enviroment/what-will-happen-when-earth-is-overpopulate (Some info)

http://howmany.org/environmental_and_social_ills.php (Some info, all images)