X Windows was designed from the ground up as a thin-client solution. It was designed to be used with multiple terminals running off one powerful computer. X windows is a client-server architecture. It's kind of counter intuitive which is the server and which is the client, but I'll try to explain it. The server is the PC you are sitting at, and looking at. The client is the big, powerful computer in the back room. The X-server runs on the local PC, and you run software on the more powerful remote PC, but displays to the X server on the local PC.
I use this *constantly* on my PC's. For years (until about a year ago when it broke) one of my primary PC's was a Thinkpad P1 133 w/ 72MB RAM. I was able to do whatever I wanted by using it as an X server and running the programs on remote clients, which were more powerful and did the bulk of the work.
This is what I do. I turn on the client PC, and start up X Windows. The I do "ssh <name of big powerful computer> -YXC" (case sensitive).
This then opens a terminal and forwards X over that. Now if I type in the name of an application, it's running on the other computer, but displaying on the one in front of me. It works quite well for most things. One slight annoyance is that sound isn't forwarded... I think there's a way to do that, especially with KDE, but I never bothered.
Also, anything which uses direct hardware graphics acceleration won't work. The remote PC doesn't have direct hardware access to your local PC's graphics card, so sometimes multimedia can be slow. Other things work quite well. You need a decently fast net connection (100 mb is good enough). You can maybe get away with a bit less, like 802.11g.
In general, different architectures will work fine with each other. In other words, a PC running Linux can ssh into a BSD box, and everything will probably work fine (although vastly differing X servers can *sometimes* not get along. Overall though, the protocol is standardized across architectures.
You will need to enable X11 forwarding. This is usually in a file like /etc/ssh/ssh_config or /etc/ssh/sshd_config, and you will need to make sure the ssh daemon is running on the machine you are connecting to. Restart ssh after changing the X11 forwarding settings.
Linux computers, unlike Windows computers, are built to be interconnected and interoperable, and they are very easily adopted to client/server and thin client approaches with minimal effort.