In general there are two flavors of X desktop. The two most famous "heavyweight" desktop projects are GNOME and KDE; these include both a desktop environment and an application development framework. A desktop environment includes a window manager, help browser, file manager, task bar, and so on. A development framework includes any number of libraries to ease application development, perhaps most importantly a GUI toolkit. GNOME and KDE are the desktops with the most support from Linux distribution vendors.
The second flavor of X desktop includes a desktop environment only; no development framework is included. The line between this flavor of desktop and a plain old window manager is a bit blurry; many people would describe Xfce, WindowMaker, and Enlightenment as desktops in this category.
Desktops can be mixed-and-matched; for example, you can run Enlightenment together with GNOME or KDE components; you can run applications developed with the GNOME or KDE development framework under any of the X desktops. One purpose of freedesktop.org is to ensure that this mixing-and-matching remains possible, and promote more of it. Read our Mission Statement for details. The executive summary is that people or organizations developing applications do not need to worry about which desktop their users will select. Applications which work with any desktop are easy to write.
One way to think about the mission of freedesktop.org is this: to ensure that the different development frameworks aren't user-visible.
X Desktops with a Development Framework
Backbone: A GNUstep-based desktop environment
Étoilé: another GNUstep-based Desktop Environment
GNOME (developer site): The GNU Network Object Model Environment
KDE (developersite): The K Desktop Environment
Plain Desktop Environments
AfterStep: Window manager that combines flexibility with elegant look
awesome: Highly configurable, next generation framework window manager
AntiRight: Lightweight scripted environment that uses the Motif toolkit
Enlightenment: The Enlightenment Window Manager
fluxbox: Lightweight WM with support for tabs
FVWM: An extremely customizable window manager and some desktop applications
IceWM: Window manager designed to be small, fast and lightweight
Matchbox: Environment for non-desktop systems, such as handheld computers
GoFun: Lightweight Desktop Entry Specification based desktop
ROX: ROX is a free, GTK+-based, fully drag-and-drop desktop
WindowMaker: Window manager intended to work with GNUstep Note: right now (2006-10-31), it's living at www.windowmaker.info.
Xfce: Lightweight GTK+-based environment
XPde: A Windows XP-like desktop environment designed for Windows users migrating to Linux
EDE: small desktop environment, built to be simple and fast
UDE: attempt to create new WM with original Look'n'Feel
LxDE: provide a new desktop environment which is lightweight and fast
3D Desktop Environments
Looking Glass: Looking Glass 3D Desktop Environment
Metisse: Metisse 3D Desktop project
True3D*Shell: open source 3D desktop environment
Compiz: OpenGL-based 3D window manager to extend existing desktop environments like Gnome and KDE