I debated this one quite a bit, but in the end I chose the mp3 player for a couple of reasons.
First, this is a pretty universal choice. Whether you workout indoor or out, whether you run, walk, bike or even swim, an mp3 player can increase your exercise enjoyment. I generally workout to a high energy music mix, but you can choose news podcasts (I like This American Life from NPR), pre-made music mixes, or even coach-designed personal workouts with audio cues for warmup, intervals, etc., and everything in between.
Second, a little extra can sometimes be the difference in a workout. Whether that extra is entertainment, motivation, rhythm, or distraction an MP3 player can enhance many workouts. For me the little bit extra I get is focus. The music helps me shut out distractions and focus on my body and how the workout feels. It helps not let external issues interrupt my time and frankly it sometimes helps me push through the discomfort.
Lastly, many people already have one or at least a portable radio which will serve the same purpose. If you do, but don’t use it to workout, I highly recommend you try it. If I’m exercising alone, you’ll find me with my earbuds in and the music going.

I happen to prefer Apple’s iPod Nano for workouts, there’s a good mix of features and durability for the size and price. But your mileage may vary.
One safety note: if you’re outdoors please do not use an mp3 player in any way that would limit your hearing. You need to be completely aware of your surroundings while on the roads and trails. Loud music or noise-isolating earpieces can prevent you from hearing traffic, approaching vehicles, or even pedestrians. Use common sense and if using an mp3 player outdoors use open-air earpieces and limit the volume of playback.