The common use-case here is that you updated to ESX 6.5 and now you get this error when connecting:

The required client support files need to be retrieved from the server "0.0.0.0" and installed. Click Run the installer or Save the installer

But when you run it, it fails.

This is actually by design. VMware decided to go ahead and put the final nail in the C# Clients’s coffin. It has been deprecated for quite some time, but still worked.
 

Having spent a little time with the 6.5 Web Client. They switched to HTML5, which I think was a darn good choice(especially considering the previous choice was flash). The first(base) version still needed some work in order to make all of the features usable without a plugin. But after update 1(6.5u1), all of the features I previously used the C# client for, appear to be present.

One particular feature I am excited about, is that I can pull down OVAs using a URL instead of having to upload it via the C# client. This will allow me to pull down my image from a repository in the DC rather than trying to upload it from my cable modem.