You'll use Shazam more often than you'd think. While traveling, if you hear a new song that you like on the radio or in a bar or anywhere you encounter new music, you can take out your phone, and Shazam will analyze the song's waveform and match it with the correct artist and track information. You can then download the song or learn more about the artist.
But perhaps more important, Shazam is the app you show off when a Luddite asks, "What's so great about a smart phone?" It leverages just about every piece of cool technology in that little handheld wonder.
See also: Pandora, Slacker, Rhapsody