Animated construction of a regular 17-gon with compass and straight-edge.
Finding a construction that includes a proof of correctness online is not as easy, but I did find a proof of Gauss' algebraic solution. (It's not for the faint of heart, though.)

Of course, the big open problem in this area is whether 3, 5, 17, 257, and 65537 are the only Fermat primes.