Wondering if anyone has any experience or knowledge of some good, free, potentially open-source, cloud/Web Operating Systems that I can install and host on my own personal 2K8 R2 Server at home?
It sounds like what you're actually after is a virtualization solution.
By installing something like VMWare or VirtualBox, you could have several customised "operating systems" accessible remotely running on your server.
e.g. You could have a Linux console-only VM, a Windows 7 VM with Office, and a Mac VM with Xcode all running on your server, and accessible remotely.
As far as accessing these through the browser, VMWare provides a tool called "vSphere Web Access", however it requires VMWare ESXi, which is not free.
VirtualBox supports it's own RDP protocol called vRDP, however it isn't accessible through a web browser, and vRDP clients seem to be pretty scarce.
More info on vRDP is available in the VirtualBox manual, ch 7.
Alternately, you could use an OS-native remote solution. Versions of Windows from XP upwards support Microsofts RDP protocol, and viewers are built into certain versions of the operating system.
Finally, probably the best route compatibility-wise would be to use a VNC client such as TightVNC
This is a multi-platform VNC client/server which specifically has a Java viewer, which will run on any computer running Java. The server also comes with a built in web server.
From their website...