As recently as a year ago, the Linux desktop was easy to describe. GNOME and KDE dominated, both offered an ecosystem of applications, and neither much different from Windows and OS X in their goals or design. Xfce was a distant third, with other desktop environments trailing even further behind.
Now, at the start of 2012, the state of the Linux desktop is radically altered. GNOME and KDE remain popular, but GNOME has been fragmented by the rise of Ubuntu's Unity shell.
Moreover, because of user dissatisfaction with GNOME and Unity, Xfce and other alternatives are receiving more consideration -- although how many users are switching to them remains almost entirely undocumented.
What the long term affects of these changes will be is impossible to predict. Whether user dissatisfaction will continue, and which desktop environments will gain popularity as a result is anybody's guess.
For now, the most you can say is that users of free and open source software have dropped the idea that a single desktop environment can suit everybody's needs.
Instead, most user's criterion for choosing a desktop fall into one of four main categories. In terms of appeal, desktop environments are either traditional, minimalist, experimental, or -- in a class by itself -- Unity.
Although some desktop environments could be squeezed into more than one category, the appeal of each of these types is usually quite distinct. For example, someone who prefers a minimalist environment is unlikely to consider an experimental one, any more than those who favor a traditional desktop will consider Unity. Generally, the appeal of these categories rarely overlaps
Traditional desktops are the conceptual descendants of Mac and Windows -- or, on the free desktop, the KDE 3 and GNOME 2 series. They feature a configurable panel, a main menu, and a general workspace, sometimes augmented by virtual work spaces. Some traditional desktop users may be conservative, but just as many seem to think of an interface as the launcher for their applications, and to want nothing more except some basic customization of themes and wallpaper.
By far the most popular traditional environment is Xfce. You often see it described on distribution mailing lists as a stripped down GNOME desktop. Since the development team is careful to control code bloat, most distribution's versions of Xfce are faster than their versions of GNOME or KDE.
However, because usability has become an equal priority in recent releases, to call Xfce minimalist no longer seems appropriate. Increasingly, it seems the alternative of choice for those who long for GNOME 2, including Linus Torvalds. Xfce's major weakness is that it has only a small ecosystem of applications, although its ability to run KDE and GNOME applications is carefully maintained.
In GNOME 3, you can also choose fallback mode, which looks like GNOME 2, but lacks panel applets and the ability to add application icons to the desktop. In Linux Mint (and, I suspect, in other distributions very shortly), you have the option of enabling Mint GNOME Shell Extensions (MGSE), whose combined effect is to replicate GNOME 2 within GNOME 3.
Modern KDE itself can be configured to be a traditional desktop if you make a Folder View your desktop and set it to display the Desktop folder in your home directory. However, to use KDE in this way is to ignore many of its features, and many GNOME users disgruntled about GNOME 3 and Unity are unlikely to consider KDE as an alternative.
Moreover, for those who preferred the KDE 3, a better choice is probably the Trinity Desktop Environment (TDE). TDE is an updated port of KDE 3. In fact, its version numbers are a continuation of KDE 3.x's. Because maintaining and updating the code is a huge effort, and the development team is small, TDE does suffer from more bugs than you may be used to. But, in general, TDE is an example of how, in free software, nothing is ever lost so long as someone is interested in preserving it.
Minimalist interfaces have a long history in free software. To this day, you can still find long-time users who restrict themselves to a window manager like IceWM, or -- slightly more elaborately -- a tiled window manager like Ratpoison.