Its important not to ignore missing data, but researchers often do. You need to be on the lookout for potential problems caused by missing data when you read research or conduct it. How can missing data be a problem? It means that the sample that is left–the one you analyse–is no longer representative of the whole population. Its only the ones that were not missing: those that chose to answer all the questions, the animals that enjoyed eating the food, the ones that were well enough to participate in the full trial. It also means that the sample is smaller than it might appear to be and therefore that real differences may not be detected.
In this news article Sarah Hoare explains her research which investigated the inherent bias in surveys of the wishes of patients at the end of their life. She found that conclusions reached from analyses that ignored missing data may have been flawed. http://www.cam.ac.uk/research/news/missing-data-complicate-picture-of-where-patients-choose-to-die
Many clinical trials suffer from problems with missing data. Another common example is weight loss trials. You need to think about this when reading the research or analysing your own results. Why do you think those that did not persist with the weight loss protocol stopped? Could it have been that the protocol did not work? If only the data from the completing patients was analysed, could this suggest the diet worked better than it really did? Yes.