What happens when you finish the duolingo tree?

[EG01]

Do you get a certificate yet?

[Yamarrin]

You get an owl with a flag-scarf at the bottom of your tree - I just got mine yesterday :P.

A more serious answer can be found here:
http://www.duolingo.com/comment/663031

[clyde_the_camel]

Don't tell them about the private club and the discounts!

[Yamarrin]

Then the lingots for the chosen ones only should remain a secret, too? :P