I listen to classical music on my iPhone and on my iPod. I don't use an app because I find that I really mostly listen to my own music on these devices (so much so that I even wrote an eBook about it: www.classicalweekly.com/ebook . So for your OWN music from your own library, an app really doesn't add much.
BUT -- if you want to hear random classical music you can try Pandora which is great! You only get a certain number of "skips" but it's nice to discover music you haven't heard before.
Yea. The only "classical" app I have is a Piano app. It has a tiny piano keyboard than you use the touch screen to play. I use it in choir practice when I have a long pause. Just before I come in again I play the first note :D Perfect!
Spotify is a good iPhone app for listening to all kinds of music, not just classical