Just simple script that adds missing playlist functionality to HTML5 audio element.
See live demo or real world use.
Add your audio element with first song of playlist and data-playlist-id attribute:
<audio src="trololo.mp3" controls data-playlist-id="my_awesome_playlist"></audio>
Add playlist itself as list of links:
<ul id="my_awesome_playlist">
<li><a href="trololo.mp3">trololo</a></li>
<li><a href="sandstorm.mp3">Sandstorm by Darude</a></li>
</ul>
Note that currently playing song in playlist will have current-track class on link.
Include javascript file AFTER the playlist (at end of the page):
<script src="html5-playlist.js"></script>
???
Profit!