If you don't count the ads and the inability to listen to stuff unless the app is at the forefront of your smartphone screen, YouTube is as decent music streaming service as any. Frankly, Google knows that, which is why it has its own YouTube Red service that gives you benefits like offline listening and audio mode against a monthly fee. But if you don't fancy it for some reason, or it's not available in your country, you can try an app like TubeLike. In short, TubeLike lets you access all the music up on YouTube without paying anything. It's also a great music discovery tool! Feel free to browse through the News section to see what tunes are hot and just tap on any one to play its video. You can also share it, make it a favorite, or add it to your playlist.
Additionally, TubeLike has dynamic Top 100 Charts list that lets you find all the hits worldwide or in your country. Like in iTunes, you can browse familiar music categories and a trending videos list, as well as enjoy high-quality HD videos, AirPlay streaming support, and a fully featured in-app media player.
A much cheaper, but not as fully-featured alternative to YouTube Red.
The search function helps if you are looking for something specific and you also have all the trending terms displayed for you. Stealing an interface clue from Tinder (everyone is swiping it!), the Discover section lets you swipe left for music dislikes, and right for likes. Anything you like will be added to your Favorites. Meanwhile, the Playlist section houses custom playlists made by you, as well as your history and favorites.
Alas, listening to ad-free music does come with a price. TubeLike lets you remove the ads with just a one-time in-app purchase of $1.99, which is much cheaper than a $12.99/mo YouTube Red subscription. But it's up to you to decide where your cash is better spent.