Group passwords can be used to allow users to manage group memberships or to join groups they might not be a part of by default (like joining "wheel" to su, etc). You can set up group admins and such, but I've never personally found a good use for this.
I suppose you could use groups to help establish a concept of "Power Users". You can also install the "sudo" package if your distro doesn't already have it. This allows you to assign normal users access to "superuser" commands (like running the apache restart script, etc). You can create groups and such within the sudo structure as to emulate the structure you see in Windows.
Just my $.04