One of the nice things about the X Window System is its ability to display X apps running remotely on a local machine. One of the not-so-nice things about Microsoft Windows is the complete lack of native support for displaying X applications. If you find yourself working on Windows but wanting to use Linux apps at the same time, Xming can do the job. Xming is a port of X Window System to Microsoft Windows that's free and easy to use.
Xming is licensed under the GNU General Public License version 2 (GPLv2), and comes packaged as Windows executables with easy-to-use installers. If all you want is an X Window Server -- and not a complete Unix-type environment -- Xming is a better choice than Cygwin/X. It also has the advantage of more active development -- Cygwin/X hasn't been updated since 2004, according to its homepage.
Xming is trivial to install. Head to the Xming project page and find the releases section. You probably want to stick to the stable releases unless there's a feature in the recent development releases that you can't live without. Grab the current Xming, or Xming-mesa, if you have an older client that might need the Mesa renderer instead of OpenGL, and run the setup wizard. It takes a minute or so to run through the install. You'll probably also want to grab the Xming-fonts installer, which installs the core X fonts. After you've installed these packages, you're ready to start running X on Windows.
The Xming installation procedure creates a desktop shortcut called XLaunch. Double-click it and you'll see a dialog that lets you choose whether Xming displays programs in multiple windows, a single window, fullscreen, or in a single window without a title bar.
What's with all the options? Depending on what you plan to do, you may want to run several windows on your Windows desktop in order to display several different programs. On the other hand, you might choose to connect to a machine using the X Display Manager Control Protocol (XDMCP) and display an entire desktop on your Windows machine.
If you're going with the multiple programs scenario, choose "Multiple Windows." You can also set the display number at the bottom of the dialog. Leave this as 0 if this is the first connection that you're making, or set to 1 (or 2, or 3, etc.) if you're making multiple X connections. If you forget, you'll get an error when trying to start up a subsequent session.
On the next window, choose the session type. For this type of connection, choose "Start a program," and click Next.
In the next dialog, click "Run Remote" and click the radio button next to "Using PuTTY" and fill out the user and host information. If you don't enter your password here, you'll be prompted for it when Xming connects to the remote system.
Assuming all goes well, you'll get an xterm from the remote system. You can then either work in the xterm or start an X application in the xterm that will be displayed on the local system using Xming.
You can also run something other than an xterm when connecting to the remote system. In the Start program dialog, just enter the name of the program you want to run in place of xterm. It's slightly counterintuitive, because the name of the program appears in a drop-down box and looks like you'd select something from a list rather than type in a free-form name, but you can enter your own program here. I like having an xterm or other terminal program, though, so I can start as many apps as I like.
I've used Xming with stock X applications (like xcalc) and GNOME and KDE apps (like Epiphany, Konqueror, Gnome-terminal, and others) and had no problems running the applications. Other than having the standard Microsoft Windows title bar and such, these apps look just as they would on Linux.
Run an entire desktop
You can also use Xming to turn your Windows machine into a X terminal, more or less. Again, click the XLaunch icon, and this time select "One Window" or "Fullscreen." Next, select "Open session via XDMCP" on the Session type dialog. On the next dialog, you can choose to connect to a specific host, or you can tell Xming to search for XDMCP servers.
The next dialog allows you to specify additional parameters. You probably won't need to give Xming any additional parameters, but if you need to specify a remote font server, this is the dialog to do it in.
Finally, you can save the configuration if you want and reuse it later. Once you click Finish, you should see whatever X login manager is running on the system you're connecting to.
Xming is easy to use and provides an excellent X server for folks who have to run Windows. Since it's free software, it's also much better for the budget than commercial X servers for Windows, and it enjoys fairly frequent releases, so it should be around for some time to come.