You give us good information about the problem with screen dumps and a photo: very good.
The GY-521 has an onboard voltage regulator for 3.3V. If you supply 3.3V to Vcc, the resulting voltage might be a little lower.
The Mega 2560 is an older chip which requires a high voltage for a valid '1'.
That seems to be the problem.
Solution: Use the Arduino 5V pin for the Vcc of the sensor board.
Or use a level shifter for the I2C signals.
The I2Cdevlib requires an interrupt. Connect INT to pin 2 (pin 2 is int.0).http://arduino.cc/en/Reference/AttachInterrupt
AD0 has a pull-up or pull-down resistor, you don't have to connect it.
Note: the sensor board is running at 3.3V so if you want it to be high, connect it to 3.3V and never to 5V.
This is basic information to start, http://playground.arduino.cc/Main/MPU-6050
To get an i2c device working, try the i2c scanner as the first test.http://playground.arduino.cc/Main/I2cScanner