High-speed computer interface with an Arduino
It's definitely possible to get up in the Mbps range with an Arduino, especially with your Due. The serial monitor only supports bauds up to 115200, but you can use a separate terminal window which allows you to set your baud to anything you like.

For a little more information, see This Thread on the Arduino forum. 

In terms of setup, on the Arduino it's as easy as Serial.begin(1000000); or to that extent. It's all about the setup of the device that you want to communicate with, and what it can handle.