Binary counter with 16 Leds

Using Arduino LEDs and Multiplexing
4

Read - http://www.arduino.cc/en/Tutorial/ShiftOut - carefully especially the part about red /green leds at the end.

The code should be something like below (not tested)

void loop()
{
  for (unsigned int numberToDisplay = 0;  ; numberToDisplay++)  // it will automagically wrap around ..
  {
    digitalWrite(latchPin, LOW);
    shiftOut(dataPin, clockPin, MSBFIRST, numberToDisplay % 256);  lower byte
    shiftOut(dataPin, clockPin, MSBFIRST, numberToDisplay / 256);  higher byte
    digitalWrite(latchPin, HIGH);
    delay(500);
  }
}

be aware 65535 * 500 millisec = 32767 seconds, thats about 9 hours for one loop...