If I upload any sketch that sends serial data, I immediately see the TX/RX LEDs flash once the sketch is uploaded. If I then start the serial monitor, the sketch appears to restart.

A bare minimum sketch that shows this behaviour:

void setup()
{
    Serial.begin(9600);
    Serial.println("Setup");
}

void loop()
{
  Serial.println("Loop");
  delay(1000);
}

Tested with several boards and Mac and Windows versions of the IDE.

Example output - it goes back to "Setup" when I open the serial monitor:

Why is this?