It is every designer's dream when your client lets you design whatever the heck you want and actually have it brought to life. Here are a couple of great examples I found via The Design Files and ManyStuff.
Julien Vallée is a motion graphic designer/ art director from Montréal. A lot of his work are hand-sketched or hand-made with construction paper. He made this brilliant paper computer and cup for a blog called ManyStuff. It is a site that questions the relative roles of the computer and hand-made processes in design.
And from ManyStuff I found Michiel Schuurman's invitation he designed for a hotel in Amsterdam. I love how the triangle is made with just one long strip of paper and works like a puzzle. See how it unfolds below. images: Julien Vallée and ManyStuff