GDM — Gnome display manager.
LightDM — Cross-desktop display manager.
LXDM — Lxde display manager.
SDDM — QML-based display manager and successor to KDE4's kdm.
SLiM — Lightweight graphical login solution.
XDM — X display manager with support for XDMCP

Unity is the default desktop for Ubuntu, and is one of the major desktop environments.
Gnome is other of the major desktop environments.
KDE is other of the major desktop environments.
Xfce is a much lighter desktop environment.
LXDE is arguably the lightest option available for a desktop environment.
Cinnamon is another alternative to Gnome.
MATE is a continuation of the Gnome 2 codebase.
Budgie is the default desktop of Solus Operating System.
Moksha is a continuation of the Enlightenment 17 desktop.
Enlightenment started as a project to build a desktop environment.
Pantheon is the project developed by the elementaryOS team.
Trinity is a continuation of the KDE 3 series.