Another way I have found that works reasonably well is to sign up for a free Dropbox account. Put the audio files in the dropbox folder and then access them on your iPhone.Dropbox will play audio files but it's a pretty simple player.
Ron is right though, Apple goes out of their way to lock your iPhone to iTunes. It's annoying but remember that Apple sells software only to make their hardware more valuable, which is why you get iTunes (and Mac O/S...) for free. So annoying as it is, I suppose it is understandable...