Pandora and Spotify are free music services.
Pandora lets you create stations based on artists, songs, or genres you like. It will play music based on those things, so you might create a Paul Simon station and get James Taylor, Simon and Garfunkle, Van Morrison and more, not just Paul Simon. It was originally intended to help introduce people to new music, so you wind up getting more of the other artists than the artist you used to base the station around. You rate songs you like to help adjust the station to your preferences. You can use the free version with ads or the paid version with no ads. I don't know about the pay version, but the free version does not allow you to enter any song you want and play it whenever you want.
Spotify is similar, but you have more control over what you hear. You can play an entire album, hear music by only the artist you want, or create a playlist of songs you like. You can also share playlists. You can get a pay version with no ads and more options, but I've never bothered because the free service works well.
They have online versions and apps to download to devices.