In the past I used a second generation iPod Shuffle. Boy was this thing a beast. I used in in the rain, snow, indoor and outdoor double marathons, you name it. However one cycle in the washing machine and it was done for :(
That was when I went on the search for a new running music player. I looked into the current ipod shuffle, which was nearly identical, although due to a couple reasons inferior, to the 2nd generation. However because of the absurd price I decided to go with something new, the Sandisk Sansa Clip+ 4GB MP3 player and a Sandisk 16GB Micro SDHC Card to go along with it.
For less than the price of the 2GB iPod shuffle, I purchased a 4GB Clip+ and a 4GB micro SD card. I would recommend getting the 2GB player off Amazon.com and an accompanying micro SD card. For less or the same price, you get much more memory and many other features when comparing it to likely the most popular music player used by runners, the iPod shuffle.
Great battery life
Did I mention a screen?
I often will use the radio when I just feel like listening to some different music, such as during my 50 mile ultra marathon a few months ago. If an idea pops into my head I will quickly turn on the voice recorder, which actually works very well. The screen is a huge bonus over the shuffle, and the raised buttons work just fine even through clothing.
For a much more economical as well as more functional option, I would highly recommend looking into the Sansa Clip+ mp3 player for use while running or cycling.
What about ear buds? I use One Good Earbud