I'm wondering whether or not it's possible to install different desktop environments and window managements on the same OS and switch between them. If so, how?

I used to run a Mandrake box, and with that you could log out and boot with a different environment/management. Is this possible in other flavors of Linux? If so, how?

Thanks in advance

When something is possible in one distro, it's possible in all of them

Have a look around for window manager switching tools, that would be the easiest way. An alternative is to manually edit your X setup, but this can vary depending on how you start X and how your distro set things up for you. Often you can just create a file in your home directory (on my system it's called .xsession) that tells X what apps to run for you - your window manager is usually included in that list. Someone can give you more specific help if you give the name(s) of the distro(s) you want to do this with.

In most distributions (all major distributions) it is possible, though the technique varies by distro.

Debian, for instance, installs everything for you, so if you do "apt-get fluxbox" it will add a new entry to the drop-down list (or whatever).

That is mostly true in Fedora Core (rpm -Uvh fluxbox....) and Gentoo (emerge fluxbox), as well.

I believe that there are even some tools that will let you switch desktop environments without logging out... but I could be wrong.

the way that you can change it in Mandrake is also a way you can change it on other distros

there are distros that have things called "Display Managers"
Mandrake has it's own, called the Mandrake Display Manager, which is alot like the KDE Display Manager.

If you're using the GNOME Display Manager or the KDE Display Manager, you could have the option of choosing a different wm/desktop everytime you log in.

If you want to do it while you're already in, you have to kill your display manager, just make sure that your display manager isn't the foreground for your xsession. Then you could load up another wm/desktop.