Whether you're a die-hard music buff or a casual listener, Vevo should be on your radar. It's an app (and Web site) that is completely dedicated to music videos and live performances, and because the company has struck all the requisite deals with record labels and publishers, you can be confident that its entire catalog is legit. While Vevo is free to download, it is ad-supported, so you will see the occasional commercial play before your video.
Because Vevo is focused on official music videos, live concerts, and similar content, the app is arguably an even better destination than YouTube for this type of content. For instance, try running a search for a song on YouTube. You'll get thousands of search results, a large number of which are amateur cover performances, parodies, and other content that you probably weren't looking for. Meanwhile, the same search on the Vevo app will likely yield the music video that you're looking for, in addition to other related content that might suit your musical taste.
To watch videos on Vevo, you don't need to create an account. You can simply fire up the app and run a search or browse through lists of featured and new artists. If you do decide to create an account (or sign in using your Facebook account), you'll be able to take advantage of the Playlist feature, which is incredibly useful for keeping lists of favorites or maintaining a queue of videos to watch later.