Yes, I agree with Paul that if all you want is a 'web client', 'browser client' or 'web app' like Paul suggests, you have quite a few choices of HMI's with web servers that allow you to view your HMI as a simple web page.
We use the GE Cimplicity Web Server (fairly expensive) or the GE Cimplicity Viewers (require a small app to be installed on each client) for our client solutions and have relatively good luck with them.
The Cimplicity Viewer has the downside of requiring a proprietary app installed at each client.
The Cimplicity Web Client has the downside, IMO, that it runs using Java so Java has to be installed on each client instead of a proprietary viewer app. I also STRONGLY dislike Java's performance: since it is an interpreted language that must be virus-checked each time, it has the irritating feature of starting slowly with little user feedback during the startup. I just have never found a Java app I consider acceptable performance.
But back to the topic of thin clients: a web app is NOT generally what is considered a 'true' thin client in the vernacular of the thin client world. In a thin client, the OS is installed on a central server remotely from the client and the remote thin client simply presents the graphics and handles the keyboard / mouse. The OS and applications run entirely off the (redundant) central server and the thin client essentially amounts to nothing more than the equivalent of a remote graphics card driving the video. The Ethernet protocol between the virtual server and the thin client will be something like VNC, RDP, ICA or PCOip. Even in the case of Internet Explorer, IE would be running from the server, with IE's graphics being generated locally by the thin client.
So in the context of GE Cimplicity running as a thin client that would imply something like Windows Virtual Machines running the Cimplicity Viewer (not the Cimplicity Web App) from a central server. You'd create an entire OS virtual machine image, add Cimplicity Viewer and license the whole mess. The advantage is that every time you need to add a new client, you would clone the OS image, buy new licenses and in a matter of a couple minutes have a new client ready. Cimplicity Viewer would have no idea that it is running from a virtual machine on a server and being presented on a remote thin client: it would simply think its a regular viewer app running on a PC. I have built this configuration and tried it with VNC but been unhappy with the screen refreshes / redraws.
If someone out there has built a 'true' thin client architecture and gotten it to work (with RDP or PCOip), it would be great to hear from them. The advantages of being able to stamp out new clients in a few minutes, guarantee complete client consistency, perform centralized upgrades, and offer full server-based redundancy would be worth looking into the 'true' thin client approach.