The Royal Aeronautical Society

The Kremer International Marathon Competition

The Kremer International Sporting Aircraft Competition

The rules are here:

The Kremer International Seaplane competition

The rules can be downloaded here

The Robert Graham Competition

Prize: £500 (Five Hundred Pounds Sterling)

The purpose of the competition is to foster knowledge in the art and science of human-powered flight. The competition is open to undergraduates and other students of engineering, technology, human physiology and other relevant disciplines at universities, polytechnics, colleges of further education and sixth-form colleges in the United Kingdom. Any project entered must form an integral part of a course of studies. The work can take the form of experimental research or engineering design and must have a clear application to human-powered flight. Each sponsoring college may approve one entry in each discipline per year. 

The British Human Powered Flight Club Icarus Cup

Details here:

The Japanese Birdman Rally

Details here: