Spotify is good. The iOS app (haven't tried Android but I would assume the same) is lacking though. Like, you can't just browse by artist or your albums - you have to create playlists or search everytime you wanna play something. Kinda tedious, so I've made playlists for my favorite albums. The music selection is good, and you can always sync stuff from your PC that's not available on Spotify so you can listen to it whenever. I'm gonna give Rdio a go when my Spotify sub is up though, simply to see if the Rdio app is any better. I'm pretty sure they have 1 month free trials, at least Rdio does, so give that a go.
Also, Google Music isn't a bad alternative. Upload your songs once, have them anywhere, for free pretty much. If you just wanna listen to music you already have uploaded, it's good - not so much searching for any artist or discovering new music, though.
There was a post on reddit asking this same thing, and the most upvoted service was https://www.nearlyfreespeech.net/. I can't say I've tried it, but it seems reliable and a "pay for what you need," way to get the job done. Might wanna check it out.