The default mechanism for inserting a player in a post is to use the syntax:
This will insert a player and load your_mp3_file.mp3 into it.
Using the WordPress Media Library is by far the simplest way of using Audio Player. If you are using WP 2.5 or higher, you can use the Add Audio button. After select a file from your computer and uploading it via the Media Library screen, select the Audio Player option for the Link URL.
Spotify Play Button
Easily added to post or page for instant play of album, playlist or song.
Haiku minimalist audio player
A simple HTML5-based audio player that inserts a text link or graphical player for audio playback. Compatible with WP Audio Player style links, fully accessible and degrades gracefully, and includes Google Analytics tracking of audio plays.
HTML5 jQuery Audio Player
This trendy looking music player lets you add a single audio track or a full playlist to your WordPress site using shortcode. You can customise the colours of the player, and also display ratings, album cover art, and buy/download link if needed. This audio player is different from others on offer because it works on all major browsers, both PC and Mac, and on mobile devices including iPhone/iPad.