You should not connect this adapter direct to the board, as that has true 5V on RX and TX, because RX and TX are PINs from 8U2
http://arduino.cc/en/Main/USBSerialIf you have the level-shifter, that should do it, maybe digistump will tell something to it!
That adapter, balin showed, has 3.3V on the serial communication lines.
Those adapters use an CP2104 (which is the successor of the CP2102), there are other adapters out, using the FT232R, Maxim and other companies have also some of those out.
The cheap (slow) adapters are available via ebay aliexpress and others for about $2-$4.
If you wish to spent little more money, have a look at the FT232H
http://digistump.com/board/index.php/topic,1127.0.htmlThat device works a multiple devices in one. Its a normal USB-Serial to TTL (like the cheap adapters above) and also and HIGH-speed-serial protocol adapter, speaking native I2C, SPI, JTAG and others.
The big difference between the CORE-USB-to-serial-TTL adapters and the Arduino-Adapter is as following:
The CORE adapters are just a TTL-based UARTs, running the TTL-level protocol on the pins:

I hope, that the few german words in the picture above are understandable for all readers.
The Arduino-Adapter works different: The 8U2 (or 16U2 ...) connects with the built-in USB interface and simulates an virtual COM-Port on top of the USB protocol.
This happens over the Abstract Control Model (ACM) , which is defined in the USB Communication Device Class (CDC). Electrical communication is here USB.
On the atmel-CPU is a program running like a proxy: It accepts data from the virtual USB-COM-Port and output that to the serial port (which is therefore 5V) and via versa.
The proxy-program has some specialities: For example, when it discovers that the virtual com port is opened and closed with 9600 baud, it triggers the reset of the SAM3X.
The 16U2 on the Arduino DUE works slightly different, as this triggers not only RESET but also ERASE.
Those Arduinos, which have an FTDI-chip on board, are triggering the reset via the DTR-signal, which is connected via an 100nF capacitor to the reset-line, which is itself pulled high via an resistor.
To avoid the native port programming, you have the following possibilities:
Use an cheap USB-TTL-serial adapter. In that case you have to press ERASE/RESET before each upload yourself
Use something like the above mentioned 8u2/16u2 solution. Make sure that the 8u2/16u2 are running with 3.3V and adapt the Arduino-Firmware.
Unfortunatley the ERASE-Pin is not connected to any breakout-PIN (
http://digistump.com/board/index.php/topic,1216.msg5818.html#msg5818)
The third possibility is working via JTAG, which is one task, I am working currently on (
http://digistump.com/board/index.php/topic,1275.0.html)