Hi Krodal,
Thanks for your very informative playground article
I bought a GY-52 breakout board which seems rather similar to yours (same manufacturer):
I connected as follow:
VCC - 5V
GND - GND
SCL - A5
SDA - A4
and loaded your code Arduino Playground - MPU-6050
Amazingly enough, it worked first time
Now, I try to understand why it works 
No additional pull up resistors on SDA/SCL
ADO seem to be pulled down (0X68)
Would you mind checking your onboard regulator output, mine is 4.3V with 5V or 3.3V supply
according to datasheet, seems a bit high
Please check the above photo for possible pullup resistors
My final project is a new/better Balancing Robot http://www.arduino.cc/cgi-bin/yabb2/YaBB.pl?num=1284738418
Thanks again for this great job