If you not only want to point your domain to a Windows Azure web site using www.yourdomain.com but also using a naked (apex, root) domain without the www such as yourdomain.com I found that it was not fully clear how to do that. The “official” documentation can be found here:
This is how it should be to make it work
To configure an A record to enable your naked domain (yourdomain.com) as well as the full domain (www.yourdomain.com), you must configure two CNAME records used to verify the domain names. This process is the same as the one used to configure a CNAME record to point to your web site, except that you configure the CNAME record domain names that will be used for verification purposes.
For example, using the Microsoft sample domain contoso.com, the hostname will be awverify.www.contoso.com and the value will be awverify.contoso.azurewebsites.net. The second hostname will be awverify.contoso.com Once this has propagated, you can configure the A record.
As you see this is a bit different compared to the original instructions. The original instructions omit the fact that not only the www.yourdomain.com domain needs verification but also the yourdomain.com domain!
Have fun, and let me know your comments!