Lately for me it's the iOS Music app. Every iOS release it gets further away from the original purpose. Off the top of my head, the "Search" screen used to show the last 10+ things I searched for (artists, playlists, songs, etc). Now it only shows the last 3 things I searched for, and fills the rest of the screen up with what's trending on the iTunes store. I didn't ask for that!
It also regularly refuses to play music which has been downloaded to my iPhone because my cell signal isn't strong enough. I have to put it in airplane mode when I'm on the subway.