I've been uncharacteristically silent, so I'll put in
my 4 cents now.

My vote is for User Group.  Simple, economical and correct.
More on the grammar further below.

As for the images:

I far prefer the original treatment with Prickly Pears:
   http://www.zen2now.com/tux/tux_wallpaper.jpg

... because the prickers say "desert" so effectively, and
who will see this without thinking about Arizona?
Where else?  Nevada?  New Mexico?  Naw, in this one Tux
is definitely in Arizona.

And this from a guy who first encountered a prickly pear
in the wild on CAPE COD, out near Provincetown, while
working on a line-clearance crew.  But the problem is
that the saguaros just don't come out right.

Now on a coffee mug or a T-shirt, you might use a more
elaborate picture:  I'd like Tux with a flamboyant Stetson
(you'd have to put a slight shadow across his face),
standing (not sitting) next to a saguaro twice his height
that has clearly visible spines, but he's leaning on it
nonchalantly with one "hand", and spinning a six-shooter
with the other (I guess he needs a gun belt too).  Faint
mountains in the background, a hot sun overhead, and the
obligatory cattle skull in the foreground with broken
horns and a blue-green italic letter W.   ;-)

Back to the grammar:

When I see Users Group, I see a missing apostrophe.
The alternative is that it's a redundant "double plural"
as in "a group of multiple users", since group implies
more than one.

My instinct has been to read it as Users' Group, being
a group BELONGING to multiple users.  I think I've managed
to overcome my chronic EnglishTeacherItis and restrain
myself from putting it that way anywhere on the site.
I think.

For the sake of hearing myself talk . . .

Vic