Not only can you record songs on an iPhone, but with the new iPhone 3GS, you can record video.  Several people have already posted music videos recorded solely on their iPhone 3GS.  Technologic Overkill is the first one, check it out:

While it may not be the first one, I was more impressed by BSJR’s “Play” video:

This one breaks the rules. It wasn’t filmed on an iPhone 3GS, but all about the iPhone 3GS. Here’s Julian Smith’s official music video for “Got My Mac on With iPhone 3GS”: