I removed all of my gnome-panel's in favor of the Avant Window Manager for a number of reasons, and would really like to not have to have a gnome-panel still just being hidden.
Is there a command to launch the Alt+F2 window without having a gnome-panel active? I'd like to add an icon to my dock that launches that window, or a window that let's me run a command like that one.
No, the Alt+F2 window is a dialog within gnome-panel, so you can't really launch it standalone.
I highly suggest using gnome-do instead though.
To supplement Ken's great answer, I would add that the openbox window manager includes the
gnome-panel-control
program that allows you to call up the GNOME Run Dialog. You could install openbox without using the window manager and use the following command:an alternative to gnome-do is kupfer - http://packages.ubuntu.com/search?keywords=kupfer
According to here: http://ubuntuforums.org/showpost.php?p=9813331&postcount=2 there are a number of simple run dialogue programs: gmrun, Alawalk, Bashrun and Lauf. Lauf is apparently good.
Although not a launcher, you can install guake. Its a drop-down terminal, much like the consoles in FPS games where you entered cheat codes.