Wire MPU6050 (cheap eBay breakoutboard) to Arduino MEGA 1280

teckel:
My guess is that your breakout board doesn't include voltage regulators for the signal pins. Therefore, you're feeding 5v to the sensor over the signal pins and probably fried it. Get another one, but not just a breakout board but one with voltage regulators.

(Assuming you mean logic-level converters, not voltage regulators). Yes - looking at this page it clearly says the operting voltage is 2.375V–3.46V. In other words this expects 3V3 not 5V0 logic.

So it should be connected via an I2C-capable logic level converter.

On the other hand, since the break-out boad was connected to A4 and A5 which were doing nothing (on a Mega1280) the board is maybe not fried ... yet. And on the third hand, this datasheet says (on page 20):

Supply Voltage, VDD -0.5V to +6V