Spotify, Pandora, iHeart Radio, Slacker, Amazon Music, Amazon Music Unlimited, Google Play Music, Google Play Music Premium, Apple Music, Rhapsody, TuneIn, YouTube Music App (Android; iTunes)

Music on Alexa
Basic Amazon - Can play by genre or artist but not specific songs
Amazon Prime $99/year * 2 million songs See   
  https://www.amazon.com/gp/dmusic/promotions/PrimeMusic?ref=pr_ol_lm
  
Amazon Music Unlimited $10/mo ($8/mo with Prime) 10's of million songs
  
Pandora - Can play with a free account
Spotify - Requires premium Account
Some third-party music providers (like TuneIn, and iHeartRadio)

• Listen to music on Google Home
  How to play music on Google Home without a Google Music subscription
• Ways to Listen to Music & Media on Alexa
• Spotify Vs Pandora Vs iHeartRadio: The Best Music Streaming Services - Creative Music Education
• Spotify vs. Apple Music vs. Amazon Music Unlimited: Which Is Best? - MakeUseOf.com
• Pandora, Apple Music, TuneIn, Slacker Radio, Napster UnRadio - Which online radio app is right for you? - CNET 2016