By default, Azure blocks all access to your SQL Azure database, unless you specifically add firewall rules for your IP. In some cases you may need access from any IP in the world (e.g. when you want to use Remote Desktop Manager through Azure and require access from any IP). In this case, you have to adjust the firewall so access from all IP's are allowed. Here's how.
Go to the Azure management portal: https://manage.windowsazure.com/, and log in with your Live ID.
Once logged in, look for the SQL database server you wish to allow access to.
Click on the server name (not the database name) to gain access to the server configuration (and firewall settings).
Click Configure in the menu to configure the server. You'll get a list of Allowed IP addresses, and also have the ability to add one.
To allow for full access, add a new rule and like so:
This will open up public access by adding the full IPv4 address range as a range of allowed IPs.
Don't forget to change your database users to use a more complex password scheme. Public access means anyone can connect to your database server from anywhere, allowing for easier unauthorized access.