Costs me about $0.50 a month to host a simple, static site.
The free level only allows "azurewebsites.net subdomain with FTP/S and SSL".
If you want a custom domain name in Azure Websites, then you need to pay for the "shared" level (at least) and in my opinion the price goes over what any standard hosting company would charge:
http://azure.microsoft.com/en-us/pricing/calculator/
1 site, 2GB bandwidth = $9.68/mo!!