I have updated my old YouTube Playlist Player plugin to work with the latest WordPress version and to include the latest YouTube API (v3). Among the other changes, I have updated the plugin’s branding, according to YouTube guidelines.
YouTube Playlist Player Demo | Download (free)
The plugin uses a lightweight codebase and is loaded programatically, based on its location (i.e. it only loads where it is displayed, not on other pages). I have several items on my roadmap for this plugin, including several playlist styles and layouts and more customisation options.