Depends on the terrain conditions
Like one of the other posters already said, there are plenty of past threads on this topic and the opinions are evenly split. I don't consider myself to be a big risk-taker, nor overly conservative... this boils down to a judgement call based on the situation. Personally, I will have tunes going any time that I consider the situation to be safe (which is most of the time where I ride). Depending on your tastes, some music can really pump you up and increase your output... if you've tried skiing with tunes, it's essentially the same feeling. Besides, most "open" headphones allow outside noises to get through so you're not totally deaf. I use a Sony sports radio wrapped around my handlebars and an iPod clipped to the back (right side) of my shorts (headphone cord inside my shirt). I don't like cords flying around and don't like stuff hanging off my arms when riding.
The iPod is my wife's - got her a mini for our anniversary... it works great! about 4-5 hours of play time, excellent sound quality and light/small form-factor. Another key feature is the navigation "wheel" - you can reach back and adjust volume, skip tracks, puase, etc. without taking your eyes off the road/trail. One thing I was worried about before we got it was the possibility of "skipping"... no worries there... it's never had the slightest hint of a problem associated with movement (I run with it too).