The recessed can I installed have 3 wires in the junction box, black, white, and green. Do I need to run a ground (14/3) or can I just use 14/2 and leave the green empty? I am just wiring 6 can lights on the 15 amp circuit.
14/2 has three wires. The ground is not counted in NM wire. There is NM WOG(without ground) but it's not very common and you shouldn't see it in any home center. And no, never leave the ground unconnected.