What I'm about to talk about might leave a confused look on some people's faces that are not familiar with linux in the least. So I'll attempt to lay a little foundation, using windows as a visual comparison.
Under Linux, you don't just have a "Desktop" like you do under windows, which is mostly handled by explorer.exe. Under linux there is 2 major pieces. The DE (Desktop Environment), and the WM (Window Manager), and together they make up your "Linux Desktop".
Now possibly you already have an impression of what the 2 pieces do. Basically DE handles your backgrounds and icons, sometimes some other visual type items.
The WM, as the name suggests, handles your program windows... there size, location, and sometimes special effects when you move the windows. It effectively goes over the top of the DE, and in some cases with an added program to handle your "taskbar", makes your your desktop. When all is said and done, you often can't tell were one starts and the other ends.
With that said, there are a number of DE's and WM's, some combine both effectively into one package (Gnome, KDE, and XFCE). The lighter desktops (LXDE, Openbox, IceWM, and sometimes XFCE again) are sometimes easier to see the DE and WM separation. LXDE and Openbox are a common combo of DE/WM, and in many cases is my preferred desktop. It's better for older computers, or for those that like a light, snappy desktop that stays out of the way when you have work to do, and both parts can be customized to your liking. Sometimes the Openbox WM is run by itself, making an even leaner desktop with no icons cluttering up the screen. Crunchbang linux for one, is setup like this. The only real problem is that Openbox does not update the program menus when you install a program, you have to edit the menus yourself. Once you get the hang of it, it's not hard to do, and there is a graphical menu editor available that helps a great deal.
My next choices for desktops are XFCE, and Gnome. While KDE does look nice, it's speed and glitches (for my experience anyway) make it seem too much like windows, which linux is not, nor is it meant to be. XFCE can get kind of bloated if you add a bunch of the plugins and widgets, but clean it is pretty nice. Gnome version 3.x, they tried to turn the desktop screen into a tablet screen (icons for everything), and seems slower and awkward to use. If you can stay with Gnome 2, or one of the Gnome 3 projects that make an effort to make it look/feel like Gnome 2, it's pretty nice, and feels enough like windows to be comfortable. SolusOS is of the nicest examples of this. The menus resemble that of WindowsXP/Windows7, and is pretty straight forward to navigate. If you want to try a Linux disrto for the first time, pass on the Ubuntu's, and try out SolusOS. It's toted as being user-friendly, and they definitely did a good job with it. It's based on one of the older parent distros, Debian linux, so there is plenty of reference material and community help available if needed. It will run as LiveCD, so you can try it out without installing anything computer.
There are a number of other WM's out there, most common you will see is probably IceWM (Anti-X linux is a decent example), Fluxbox, Enlightenment, and JWM (what Puppy Linux uses). These are mostly light jobs, usually used in a bit more specialty distros. You need some knowledge if you want to change them beyond what the given distro has, as customizing is done by plain text editor. But if you want to make it the way you want it, one of these is definitely the way to go.