I got this comment regarding this question expressing that "if that was a-ok, why mine is not". Hence to prevent further problems with these kind of questions lets close and archive it for its historical value. The answers should be candidates to be closed for these motive.

BTW, instead of "What different desktop environments and shells are available?" (which can change and is evergrowing) questions like these should be rephrased as "How to install X desktop manager?" or "How to install X shell?". This keeps the Q&A format pretty well and offers a pinpointed help to each user. Does anyone want to know 'how many X are?' Just look in the apt-cache search X and be dealt with.

$ apt-cache search "Session Manager"
gnome-session - GNOME Session Manager - GNOME 3 session
gnome-session-bin - GNOME Session Manager - Minimal runtime
gnome-session-common - GNOME Session Manager - common files
libsm-dev - X11 Session Management library (development headers)
libsm-doc - documentation for the X Session Management protocol and library
libsm6 - X11 Session Management library
libsm6-dbg - X11 Session Management library (debug package)
x11-session-utils - X session utilities
gnome-session-fallback - GNOME Session Manager - GNOME fallback session
gpe-login - login window for the G Palmtop Environment
jack-tools - various JACK tools: dl, record, scope, osc, plumbing, udp, play, transport
kde-workspace-bin - core binaries for the KDE Plasma Workspace
lxsession - default session manager for LXDE
lxsession-dbg - default session manager for LXDE - debug package
razorqt-session - Session manager component for Razor-qt desktop environment
xfce4-session - Xfce4 Session Manager
xfce4-session-dbg - Xfce4 Session Manager (debug symbols)

KDE, Gnome, LXDE, XFCE are there. Others may be under the name of "Window Manager" or "File manager", etc. Either way, these kind of questions should go.