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, Arduino Playground - MPU-6050
To get an i2c device working, try the i2c scanner as the first test.
http://playground.arduino.cc/Main/I2cScanner