A couple months ago I posted a tutorial on How to Display Your Latest Spotify Activity in WordPress, which was based on Last.fm scrobbling. Since that time, Spotify has announced its new API.
Spotify Embed is one of the first WordPress plugins to make use of the Spotify API for embedding music. Once you have the plugin installed, all you have to do is paste a Spotify link into your posts and the plugin will insert the Spotify Play Button for you.
Check out how easy it is to use: