There is no age limit to compete in olympics. For few games have age limits for safety reason:
Boxing(17-32),Diving (Min 14),Gymnastics (Atleast 17),Judo (15 Min),Soccer(under 23),Weight Lifting (Min 17),Wrestling (Min 17).
Now the rules are that you must turn 16 the year you compete. So 15 years olds are the youngest competitors that are able to compete in any olympic event.
Every Olympic event has their own particular age requirements, so it is necessary to research the particular event that a person is interested in in order to find out what those requirements are.