Shazam is one of my favorite iPhone apps, and it was one of the first I downloaded from the App Store. Every time I'm in a store or listening to the radio and hear a song I like but don't know, I let Shazam listen. The free version is still in the store, but just recently they've also released Shazam Encore and (Shazam)RED, two paid versions of the app that offer up more functionality (the RED version gives part of the purchase price to charity). Among that new functionality is Last.FM integration: now, you can apparently send any songs you "tag" straight over to the Last.FM app (assuming you have it installed), and make up a radio station directly from there. Pretty slick, and the iTunes description for both apps says that Pandora works as well.
Unfortunately, reviews for the paid version say that the app still includes ads (a weird choice for a paid app), and there are a few reviews that even say the app crashes occasionally (though I've never experienced the problem of it not finding a song for me -- even with rarities and b-sides, it's always come through). But it's a real shame that reviewers are having problems -- while Shazam definitely needs to find a way to monetize its service, failing to provide a premium experience on a premium app obviously isn't the way to do it. Still, if you made the jump to the paid app already, or use Last.FM and/or Pandora often, it might be worth a look.