This single app is cooler than anything my entire phone can do (as discussed here: http://www.lunch.com/Prime/Treo_700wx_Review-Almost_a_great_phone-371). It does one task and it does pretty well. When you start it up, you press a button to start it "listening". At that point, you either sing/hum a song to it, or hold it up to a tv, radio, etc that is playing music. After a few seconds (usually about 5~10) it will come back with a list of possible matches for that song. When I tried it out with the radio, it was dead on.
Once Midomi has identified the song, you can then click for details about the artist, album, etc, or even tag the song to be purchased on iTunes the next time you sync your iPhone.
This app reminds me a little of how I felt about Tivo when it came out -- It just does what it is supposed to do so well, that you can't help but get excited about it. Even better, this app is free. I would imagine ad supported versions are on the way, but perhaps a kick-back from iTunes is enough to keep this app Ad free. There's a lot of crap out there in the iPhone App store right now, and it's great to see a free gem like this rise above the rest.