LEDs on TX/RX lines interfering with the programmig of the device
I just found this reference (using ICSP for output as well as programming -- essentially the same thing), and it suggests a 4.7kOhm.

I didn't have a 4.7k handy, and used a 15k instead and it works. 

In my scenario, I have run a sketch with a polarized buzzer connected between RX (digital 0) and GND. When connected directly (with no resistor) the sketch fails to load (but the buzzer works as expected). 

If I put the resistor in series with it, the sketch uploads without fail. 

You also probably realise, but mentioning for clarity/completeness, you will lose all serial port functionality for debugging purposes and won't be able to use Serial.[anything]. Make sure to not even initialise the port.