one resistor can be connected to multiple LED's.
The important part is that whatever current passes through the LED's also passes through the resistor (which is why the resistor has to be in SERIES, not PARALLEL to the LED's). the idea is that as the LED's warm up, their resistance lowers, which would allow more current to pass. The series resistor will "feel" that rise in current and create a larger voltage drop, reducing the voltage available for the rest of the series branch, and effectively reducing the current in the LED back to what it should be.
Without the resistor the LED would just warm up and start passing more current than it's rated for. This means shorter life, and in most cases a shift in emmitted frequency (not such an issue for moonlights, but if you're wanting to make an LED array to supplement the PAR in your day-lights this could be a serious concern)