I had a frustrating time trying to get a PCA9685 working-- it wouldn't even reply with its register byte values. I've interfaced with other I2C chips and didn't expect problems, but trouble was all I got.
Poking around the Arduino Forum trying to find any examples with a PCA9685, I found the thread on Elco Jacobs' new ShiftPWM library to drive the outputs of the ubiquitous 74HC595 shift register with 8-bit PWM precision. His demo video is on the right. The example sketch was so straightforward, I had two chips driving-- and dimming-- 16 red LED's in minutes.
Once I saw those red LED's cycling, I considered that part of the project done-- thank you, Elco!-- and started laying out a driver board with a 74HC595, eight outputs hooked up to MOSFETs and test LED's, and screw terminals so they can be daisy chained. With the DorkbotPDX order deadline this morning, I had to stay up late laying it out and getting a final Eagle brd file ready, and hopefully it will work; I wasn't that excited about asking for six copies of a 3.9"x2.1" V001 design and having no time for a second run if they don't work, but... hey, they'll work!
Here's the Eagle schematic: pdf, sch.
And the board: pdf, brd.