Many mobile devices are equipped with FM capabilities, often packaged in the same chip with Bluetooth and WiFi. Unfortunately, the FM functionnality is often disabled or hardly accessible for third party developpers.
The Communications Research Centre (Canada) developped an Android library to access the FM-RDS capabilities of the Samsung Galaxy S (some models only). It is the same library that is used in the "FM TwoO" Radio App (look on Android Market/Google Play). You can find this library on their website, with documentation and tutorials: http://mmbtools.crc.ca/content/view/53/33/.
You might also be interested by this: BlackBerry has a FM radio API now (since BlackBerry API 7.1.0.). Hopefully, there will be an FM Radio API for Android soon.
You will also find quite a lot of info about FM Radio hacking on Android on this site: http://www.xda-developers.com/.