Many running races advise against it, and if you get into triathlon, it is a definite rule violation (time penalty, possible DQ and they may take it from you).
Reason #1 is safety. Esp. in a larger race you really need to be able to hear other people around you and be aware of your surroundings. Wouldn't it just suck if there was a cone in the middle of the road that you didn't see because of crowds and you couldn't hear the runners ahead of you shout, "Cone!" and you tripped. (just as an example).
Other thing about safety...and that is women out walking/running alone with headphones. You still have to be aware of any dangers out there.
Note, I am saying that as a woman who runs with my Ipod alone sometimes, but I keep my awareness up. (so I'm not all perfect or anything)
And on another note: there are many people who get dependent on their tunes. I can totally see that...it makes running so much easier feeling! But then, what do you do when you get to a race (like I said above, esp. triathlon) where you can't have it? Then you're stuck. So it's a good idea to wean yourself from it so you can function and get your run in with or without tunes.
As for me, during a race, I wouldn't wear them...I like to hear the crowd cheering and know what is going on around me. (and as a spectator, or runner, I have a hard time encouraging the runners with Ipods, though I would like to, but I just would waste my breath because they can't hear me

).