Do photon’s have mass?

My grandmother in Burlington, IA had this massive house overlooking the mississippi there. In the windows, she had these ornaments – little glass bulbs with pinwheel looking things in them that spun and spun and spun in the sunlight streaming through the huge windows overlooking the river.

Years later in college, I learned that the window trinket was a classic science experiment regarding photons having mass. I saw one on think-geek some time ago, and got one for my house: