It is possible to have a CNAME directed to an Azure free website for about $10/month (in shared and Reserved modes). I've tested it and it's working perfectly, after the little DNS dance for the naked domain. This was the missing piece to Azure for some small sites I run.
You can find all the info here: http://weblogs.asp.net/scottgu/archive/2012/09/17/announcing-great-improvements-to-windows-azure-web-sites.aspx