What helicopter has the most rotor blades?
Special mention for Raúl Pateras Pescara de Castelluccio (good article) who was fond of lots and lots of rotor blades, settling on sixteen for most of his designs, although his Model 3 had twenty.

Pescara's helicopters may look a little comical (and dangerous!) but they are an important part of early helicopter evolution, pioneers in the first fully controlled helicopter flights, as well as the first use of the what would be recognised as modern helicopter controls.

Here's a video of Pescara testing one of his helicopters in 1922 wearing a Homburg hat with about 5mm of clearance to his head. He had many setbacks, but persevered. It's visionary, brave guys like him who make advances in aviation.

Plus, loads of blades.

Here is his Model 3 from 1929: 
(source1)