I ran without headphones during my first race and it was fine. However, I have used headphones for every single race since then. I find that having music helps me psychologically when I need a boost. For instance when I ran the 2012 Wine & Dine 1/2 at WDW, I had a specific selection from The Dark Knight set to come on around mile 8, which I had read was a bit of a challenge. The energy boost helped carry me through it.
However, because of the safety concerns, I always keep the volume fairly low so I can hear course announcements, CMs, other runners, spectators, etc.