It depends on the LEDs forward voltage and the LEDs forward current.
If you know the specs of your LEDs you can use [
this] calculator to design a parallel array.
Note, you want to keep the total current drawn under 500ma so you don't damage your PC.
If I put in the specs of some of the LEDs I have into that calculator (3.4V, 30ma) it looks like I would theoretically be able to connect 16 of those LEDs in parallel whilst drawing 480ma.