I agree with Ed and would add the following: Fate usually implies a preordained course of events which is totally outside of your control. In much mythology your fate was determined by three sisters, for example, the Moirae of Greece or the Germanic Norns. It was the fate of Oedipus to sleep with his mother and kill his father. Destiny is also a predetermined course of events in your life but you are able to take an active role in shaping your destiny. It was Plato's destiny to become a great philosopher.

They are similar but with a difference in mood. Destiny tends to be more positive: You achieve your destiny if you are lucky. Fate is more negative. It was his fate to always finish second. You wouldn't use fate in the first sentence or destiny in the second.