Sundial (solar clock) in a binary star system What would a sundial look like in a binary star system? What is the path drawn by the shadows? 

It probably depends on the system, the sizes of the stars, their distance... If you know a binary star system for which a sundial would look different from what we have on Earth, we can take it as an example!

Edit: thank you to barycarter for bringing to attention that the Kepler binary stars would look like one star from the surface of their planets. However, there must be, somewhere, a binary system where both stars are visible, such that the shadows are affected.

EDIT2 : A Google search shows that this question has been answered before, but all links to the answer are dead. - I searched "binary solar system clock", found a link by a "Charmaine Pauls" - 
But after using "sundial" instead, I found this pintrest artwork, but it is not much help. It doesn't seem to be scientifically motivated.
The sun forms a useful basis for measuring time because to a reasonable approximation it stays put, and the rotation of the Earth causes it to traverse the sky once every 24 hours. 

Provided the planet is spinning, a normal sundial can be used, but may not be quite as regular as on Earth.

A binary stellar system can have one of three possible configurations: Two stars in a close binary, with a planet orbiting at a much greater distance. This is the "Tattooine" configuration. Everything has a double shadow. A regular sundial can be used but it is not as regular, as the positions of the two stars changes as they orbit each other. 

The second configuration is a planet orbiting a star with a second star at a much greater distance. If Jupiter had been a star this would be the second configuartion.  The secondary star would be much weaker, and a regular sundial could be used. The shadow from the secondary would just be ignored.

The last configuration is like the second, except the planet is in orbit around the smaller star. The more distant star is stronger, and compariable in brightness. In this situation it is quite likely that the planet is tidally locked to the star, so a sundial isn't useful for telling the time. The slow motion of the distant star might give a long day (which could last many years) to the side of the planet that faces away from the nearby star, followed by a long cold night. This would be a challenging planet on which to live.