Why doesn't my Azure virtual machine show up in Visual Studio's Publish feature, for an ASP.NET MVC app?

The reason the VM does not appear in the Select dropdown list is probably because:

1. web deploy is not setup on your VM that is already provisioned on Azure, or
2. not allowed through firewall for inbound connection or
3. the web management service is not started or
4. it is a windows 8 or 8.1 system
5. [Update] You have an outdated version of Azure SDK (This was the issue in my case). Get The latest Azure SDK Here: http://azure.microsoft.com/en-us/downloads/
6. OR Download it using Visual Studio itself from Menu option Tools > Extensions and Updates (assuming you are using VS 2013)

The following article describes all the steps to setup web deploy publishing on a windows server system: Troubleshooting Web Deploy problems with Visual Studio

The following article describes Web Deploy cannot be setup with Windows 8 or 8.1 system. Installing and Configuring Web Deploy on IIS 8.0 or Later

Hope this helps someone.

The simple answer was to use the IIS component installer application to install WebDeploy. Once WebDeploy is installed, and the ports for it are opened on the firewall, Visual Studio will be able to publish to that machine. Visual Studio's publish dialog may be empty for a few seconds, but I think it's downloading the details of the machine or something, because it will eventually appear in the publish-to drop-down.