(Note: I do not use Apple, so iTunes is not included here. I am also only listing options that can be accessed online -- everyone has their own favorite music player for listening offline)
1) Last.FM: Though Last.FM has made some changes recently, it is still one of the best ways to listen to a variety of chosen music (picked by genre, tag, musician, etc.). Unfortunately, the biggest setback is that you cannot listen to a straight album on Last.FM.
2) Amazon Cloud Player / Google Play: Unless you subscribe to Google Play, these are only good if you have either purchased music from one of these digital venues or have uploaded your music to their respective clouds. You can scrobble them if you use Chrome and download the "Last.FM Scrobbler" extension. If you have music available on one of these resources, though, you can listen to your music commercial-free.
3) Spotify: Before you consider using Spotify you should read Sam Rosenthal's thoughts on why Spotify is hurtful to the music industry. Because of this I refrained from using Spotify for a long time, but I have recently begun to use it to listen to music I already own. My rational is that if I have already purchased the music, the musicians will gain no more money from me every time I listen to said album. If I listen on Spotify, however, the musicians will at least earn a few more pennies for my music plays. Spotify does, however, incorporate occasional commercials if you do not pay for a subscription. It can also be scrobbled with an in-program extension, which is linked on the Last.FM website.
4) Pandora: I have put Pandora low on my list because it has several issues. I used to listen to Pandora frequently before better options became available, but Pandora does not let you skip more than five or six songs, yet has a tendency to play the same tracks over and over again. At times you may hear the same obscure song that you made the mistake of giving a thumbs up three or four times in the same hour. I do still occasionally go to Pandora, though, because it is a good way to find new music. It can also be scrobbled in Chrome with the "Last.FM Scrobbler" extension.
5) YouTube: This is my final resort music option. I only use YouTube when I can't find the super obscure band I want to listen to anywhere else. Music on YouTube is usually illegal, and the musicians do not receive any compensation or royalties for the songs you play on YouTube. If you must use youtube, however, it will scrobble with the "Last.FM Scrobbler" Chrome extension. You also have to either create a playlist or search for your songs one at a time when you use YouTube. This is not a method I recommend.
I hope this helps anyone who is looking for a digital music listening venue. :)