Music Banter - Your favorite player

Hi there!
I hope this thread will be really hot to discuss!

Last week I was presented an iPhone. It is absolutely new for me because I used to have an Android-based device. Since I use my phone for listening to music I extremely need a cool media player (or a set of players) for my endless playlists.
Sometimes I listen to music on YouTube in background mode, so If you know any really handy YouTube players - please, give me suggestions.

What apps do you use for listening to music on the go and why do you personally like them?

So what I have found so far.

Watch & Listen

I have chosen it from tons of similar apps because it seems to be simple and easy to use. The aim of the app is to find new music videos on the Internet and watch or listen to them on user’s device. However, it is not a downloader.

The advantages:
Handy playback (I can switch tracks from my lockscreen easily);
Several modes for listening;
Lots of useful options that help me to find and organize YouTube playlists;
Some options for network traffic control.

You can find it on App Store easily. Unfortunately, I can't publish links

I downloaded it yesterday and I am going to use it for a while to see if it is convenient enough. I will share my experience with you.

If I find any other apps I will inform you, too!