Windows Azure VM Remote desktop connection issue

RDP port (3389) is widely blocked from network administrators of most corporations. What you need to do is either of:

• Talking with your network administrator at work and ask for permission to use RDP port to connect to your Azure Virtual Machine
• Configure different public port for the RDP Endpoint. Setting it to 443 (the HTTPS Standard port) or 22 (Standard SSH port) might solve the issue without contacting system administrator

Of course, if you use that VM for Secure Web (which works on 443) you have to chose another port number.