Pandora's app was one of the iPhone's best of 2008 on iTunes, and while I've only recently started using it, I have to agree: even over EDGE, it's a great way to get some music you've never heard on the iPhone. And they aren't sitting on their laurels, either -- they've just updated the app to version 2.0, and it's better than ever.
New in this version is the ability to access a progress bar for the songs you're listening to, and the option to create new stations from songs or artists right there in the app itself. It's definitely worth a look [iTunes link], and you can't beat the price of admission (still completely free).
I've followed Pandora from the beginning, and they've constantly updated both their website and their features since they first released -- it's all developed into a really impressive set of functionality for listening to and finding new music. They have suffered some rumors of shutdowns, but hopefully those rumors are just that. Between the remarkable set of functions on their website and this iPhone app, they're becoming more and more invaluable for serious music listeners.