Apple intentionally sells iTunes songs in "FairPlay" protected M4P format, partly to prevent songs from being played on non-iPod hardware.
There are a few open-source projects that have been set up to create software that circumvents the file restrictions and converts songs so they play back on other devices. However, most of these programs will not work with version 6.0 of iTunes or later, and many of the authors have been slapped with lawsuits from Apple.
If you want to find out more about the software that (theoretically) allows you to play back iTunes-purchased tracks on non-iPod players, Wikipedia has a good summary of the applications on its FairPlay page.
There is one way to turn protected M4P tunes into MP3s -- you can burn the songs to an audio CD, then rip them back into your liubrary as MP3s using iTunes' CD import feature. It's a hassle, and the recompression of the files is likely to result in loss of quality, but it will give you unprotected files in MP3 format. Whether it's legal is another matter -- the waters here are pretty murky.
Basically, there's no easily accomplished way to play those songs on your phone, and most methods infringe copyright law. This is one of the reasons why Apple's iTunes digital rights management system has been a subject of controversy and legal action.