New jailbreak for iPhone, iPod Touch and iPad
There hasn't been an untethered jailbreak for the iPhone since early 1.x versions (which Apple shut down quickly) but the so-called Spirit jailbreak has now been released which will let you bust open anything running versions 3.1.2, 3.1.3, or 3.2. Note this isn't a carrier unlock, it's a jailbreak which means you can access the root of your device and run Cydia apps etc.
Make sure you do an iTunes backup and then back up your SHSH blob - this basically means that you will save your current firmware state so that you can always roll it back if needed. There's a few ways to do this but one of the most popular is Firmware Umbrella - [iClarified Guide].
You can grab the Spirit app to get started here: Jailbreakalicious