Shazam is one of the first apps I actually used in context on the iPhone, and while we haven't heard much about the app since it debuted way back in the early days of the App Store, apparently the company itself has been blowing up, thanks to the free app. They've picked up a nice round of investment from venture capitalists, and the service itself now boasts over 50 million users (by comparison, Last.fm claims only 30 million, but they've gotten way more press than Shazam's service, including recent integration on Xbox Live). That's a heck of an achievement, and Apple is a huge part of it -- not only did Shazam make a big splash on their iPhone app, but they say that Apple actually helped connect the VCs and the company together. That's an interesting peek behind the scenes at what Apple is doing for one of the App Store's oldest and most popular free apps.
As for why Shazam is so popular, the VCs say they can see the platform as a "springboard" for selling music, advertising, and a few other commodities. Currently Shazam's free app only lets you tag five songs a month (a limit I never hit and thus didn't know about, even though I would say that I do use the app regularly), but they're planning a paid version that will allow unlimited identification of songs through the iPhone's microphone. I don't know how well that will sell (it's hard to believe that people will pay $5 for a service they are already using for free, though perhaps I'm underestimating the amount of music that people want to "tag"), but it's clear that Shazam is a company that is making the absolute best of having an extremely popular free app on the App Store.