"Ockham's razor" is a methodical principle, due to the medieval philosopher William of Ockham, who mainly opposed an unjustified creation of new terms in philosophy. Since this principle and its later versions are frequently quoted in discussions about anomalies, it will be studied here in some detail. After a short look on the historical roots, the principal modern formulations are summarized. It will be shown that a demand for "simplicity" cannot be generally maintained. Rather, striving for simplicity can conflict with other essentials of scientific method. Ockham's principle - no matter whether in its original or in a modified version - cannot be helpful in a rational decision between competing explanations for the same empirical facts. An incorrect use of Ockham's razor only leads to a perpetuation and corroboration of existing prejudice, and this principle should not be used to easily get rid of unwelcome data or concepts.