Arduino Uno RX/TX pins
The TX and RX on the Digital 0 and Digital 1 pins are designated for connecting to your own serial devices, whether a USB cable is connected or not. From the official Uno page:


  
  Serial: 0 (RX) and 1 (TX). Used to receive (RX) and transmit (TX) TTL serial data. These pins are connected to the corresponding pins of the ATmega8U2 USB-to-TTL Serial chip.
  


Also:


  The RX and TX LEDs on the board will flash when data is being transmitted via the USB-to-serial chip and USB connection to the computer (but not for serial communication on pins 0 and 1)


Of course, you can also use the SoftwareSerial library to communicate with serial TTL devices on any GPIO pins you like, not restricted to D0 and D1.