MPU6050 SparkFun Breakout to Arduino Uno - No Communication

kas:
...
Thanks for your very informative playground article
...
Would you mind checking your onboard regulator output, mine is 4.3V with 5V or 3.3V supply
...

I'm glad my sketch did help.

I have a good multimeter. My +5V is 4.95V and the 3.3V of the breakout board is 3.31V.
Also the XDA and XCL of the sub-I2C-bus pins are 3.31V (I think they have a pull-up somewhere).
My MPU-6050 is connected to the I2C via a level shifter, so I have not current flow from the I2C to the MPU-6050 voltage.
Can you measure the SDA and SCL (while not active), and check the XDA and XCL ?

Your breakout board has 10k pull-up resistors to the 3.3V.
That should be 4k7 to be safe.
I think that it might perhaps cause the higher voltage.
Can you add another two pull-up resistors of 10k from the SDA and SCL to the 3.3V of the Arduino board ?

The 4k7 prevents that the internal pull-up resistors in the avr chip (on the Arduino board) raises the voltage of the I2C too high for 3.3V devices.

I have added your GY-52 breakout board : Arduino Playground - MPU-6050