I just created a new Ubuntu 14.04 virtual machine in Microsoft Azure using the (recommended) resource manager deployment model. The following screenshots show the deployment
For the ones that still struggle with the inbound rules on the new Portal Azure, you need to set up the Network Security Group (NSG) to:
any
sources
and
*
- for the source port range (extremely important as it may seem normal to set 80 or 443 - which is not correct)
any
and
80
- as the destination port range (or the port that your webserver is listening to - it could be also 8080 or other)
The same goes for other ports like the 443 for the https connections.
What is your source port on your NSG? Did you leave it Any/*? If not you are limiting yourself to traffic coming only from that one port.