I got tired of my old MP3 player WinAmp, even though it is a good FREE player. The method of shuffling playlists was clunky to me and it seemed the "shuffle" too often played songs in the same order. I went to the Google Play Store and tried many of the players listed at the top. CONCLUSION: If all you want is my recommendation, here it is right up front:
Best MP3 Player for Android: PlayerPro and PowerAmp (TIE)
Both PowerAmp and PlayerPro have a lot of slick features, an easy-to-use and mostly intuitive interface, and do a a better-than-average job with the album art, which is evidently not easy to get working with files from various sources.
My first instict was to say I liked PlayerPro better, if only because the layout and design suited my personal preferences. I had been using the player during work with it sitting on a Aux-enabled radio. Later, however, when trying to use PlayerPro in my pocket with headphones, I had trouble with the player (or widget) getting activated and skipping around. For that kind of use, where I don't even see the interface, PowerAmp was superior because of an extra "Lock Screen" option.
I would recommend either one, or both, as they are both a small, one-time fee. The screenshots below are named for the screen they show. The order is: Player, Library, Equalizer, Settings, Widget.
Good FREE Player for Android: Rocket Player
If you are going to not look at your player while it's playing, and don't care about album art, then Rocket Player could be a good solution for you. I think you can keep using the free version indefinitely and it has a lot of great features like the two players above. The paid version, however, is not as polished as the two "winners" above, as the app suggested I go and get a 3rd-party application to handle the album art.
Honorable Mention: NRG Player for Android
I single out NRG Player because I think it looks So. Freakin. Cool! If I had a spaceship, this is what my MP3 player would look like. It also has a 1-touch access to playing your playlists. I almost paid for a copy but then wait, what? It ONLY has access to playlists and you CANNOT choose to select "Play by Album" or similar. You add songs to the playlists one at a time? This is the best looking player but needs a lot of work. They actually said on the website they don't display album art because the playlist is soooo much more important. C'mon, man, integrating the album art is hard, but don't BS us like we're idiots.
All The Rest MP3 Players
Here are some of the other players that I looked at, that were at the top of a search for "MP3 Players", in the Google Play store. The first one, called "Music Player", has a bunch of beautiful wallpapers but lacks features. I could not find out how to play a Playlist. All the rest of the players seem to be clones of the same source code (the Google one?). Google Play Music has some basic funtionality, but is really a joke when it comes to features. The only way that this player winds up in a "Top 5 Players" list is when some corporate shill is getting paid to write the article, in my opinion. It is nothing special and shows the wrong album art.
Google Play Music Clones: I am giving as much time to reviewing these as the developers did in coding them. There is not even one "ABOUT" link for the rest of the players, so I have no idea who made them! If you long press on them in the Apps list, and choose "App Info", it will show you the name and version of the app. The problem is they are all called "MP3 Player". So... I have named the pictures by their icons ("Green Square", "Pink Circle", etc.). Even if I loved the app, I would have to do a reverse look-up in the App store to try and figure out who made it. That doesn't seem very smart...
NOTE: If you think you have a great player that I missed, or something worthwhile to add, then you can Contact Me and I'll eventually take a look and maybe include it in this page. Thanks.