Price: free Download on the App Store
Originally known for their iTunes plugin called "AudioScrobbler", the idea of LastFM is to suggest music based on what other people listen to. So, for example, if you like Bob Dylan, LastFM would recommend Neil Young, based on the fact that other people who liked Bob also liked Neil. In contrast, Pandora's algorithm uses trained musicologists to determine what sounds like what.
Both approaches work well, and produce (surprisingly) similar results. LastFM's interface is different, though, incorporating a "similar artist" tab, that Pandora lacks. This makes "station surfing" fun and enjoyable. Plug in your headphones, and conect your iPhone to a power source and you can easily spend hours just discovering new music.
Another nice feature is the integration of tour dates. You can easily see the tour dates for artists you like and signal to the community whether you will be attending. Artists bios are also available, but not for all artists.
Overall this app is a great addition to your iPhone library. If you like Pandora you will love LastFM.