Audio
As someone who listens to music on a near-constant basis, I find the stock iOS music app to be... lacking. I'd like more features for discovering and tracking what music I'm listening to most frequently, and even suggestions when I open the app based on what type of music I normally listen to at certain times of the day/certain days of the week.
It'd also be great to have a single app that could integrate various sources all into one- I pay for Rdio and Spotify subscriptions but they still don't have all the music I listen to and therefore I keep a sizable collection of music stored locally as well. Finding myself constantly switching back and forth between apps, it'd be nice to be able to build up a single seamless queue of music, regardless of where it's coming from.
And finally, I have no idea why Apple still hasn't brought that fantastic adaptive artwork UI from iTunes to the iPhone.