A sneeze is caused by the body trying to remove something that is irritating the nasal cavity. To do this, it contracts many respiratory muscles instantly to create a powerful expiration. This produces a gush of air and the foreign material at a speed of over 150km/h, which can spread saliva and mucus at a range of over 2m. Therefore, not putting your hand over your mouth during a sneeze is an easy way to spread infections like the common cold.
An interesting fact is that one cannot open their eyes during a sneeze. This is not because of the urban legend that the eyeballs pop out if the eyes are open when sneezing, but part of the reflex and powerful contraction of muscles. Also, pinching between the two nostrils very hard can stop a sneeze reflex successfully.
Lastly, although sneezing is usually due to breathing in an irritant, some people have what is known as a photic sneeze reflex (also called the ACHOO syndrome), wherein they sneeze when stare into bright light such as the sun.