I also like to listen to music while I ride (more on that below) and am always looking for a good solution. Here is what I have found:
1. The iHome iHM4. I have an earlier version of this. The new one sells for $50 on Amazon but I got mine for $12 last year. The new one runs on AA vs AAA for the older one - that is good. There is a clear membrane so you can work the controls on an iPhone or touchscreen music player. It is heavy but sound is good. Battery life is very good - more than 8 hours - though you will notice a lot of distortion at high volumes as the battery voltage drops. It is pretty weather proof - I would not worry about my iPod in a solid downpour though the device itself might not make it. I just bungee mine to the top of my handle bar bag. No external volume control so you have to use the mp3 player volume. It does have an external power button which is handy for those times when you are stopped at a light in mixed company and your playlist delivers some inappropriate lyrics.
2. iHome IH85B. Sells on Amazon for $60. It is made for bikes and fits in the water bottle holder. It has a remote that mounts on your handlebar. A friend had one and it was a bit fiddly. Only works with iPods and not all of those so check (no Touch or iPhone I think). Only one speaker but that is all you need in these small devices as you won't get enough separation for stereo to matter. Sound was good - both bass and treble. I don't like losing the water bottle holder though (I like water as much as music). Also it is bound to pick up a lot of road mung.
3. iLuv iSP110. Around $6. Also have a friend who swears by this - he velcros it to the top bar. Volume is okay although sound is tinny as you would expect but that doesn't matter much when you are riding. Battery life is good since the amp is small. Much lighter weight than this.
4. Stuff I haven't tried: http://www.cyclesound.net/
RAGBRAI tested. Seems like it would do the trick but it's $150. I've seen a few of them on the road but none of them on.http://www.biketrailershop.com/blog/2008/08/billy-the-boombox-custom-music-bike-trailer/
A RAGBRAI staple.http://www.nytimes.com/2007/11/29/nyregion/29bikes.html
This is what I really want.
There are tons of other alternatives that pop up on google. If you have other solutions I'd love to hear them and see a review.