The icon/gui comes from nm-applet (that's the name of the process, too), a taskbar applet distributed in the network-manager-gnome package, which contains hooks for the network-manager package (network manager infrastructure.) Network Manager (not the applet) does most of the "automatic" work behind the scenes. Aside from providing functionality to nm-applet, network-manager gets used by a bunch of other GNOME apps -- for example Pidgin uses it to check for connectivity per a given polling period.
I do not recommend getting rid of network-manager entirely, as it's unnecessary to do so and will probably only cause heartache (though rare) down the line. network-manager-gnome is what you want to go after. You'll want to setup /etc/network/interfaces appropriately and probably install the ifupdown package. relevant commands then become ifup, ifdown, ifconfig, dhclient. Perhaps have a look also at /etc/resolv.conf.
I personally find the nm applet invaluable for wireless, but it can only do harm on a desktop imho -- on a workstation or server you'll want as a simple and static of a network setup as possible and convenient. (e.g. your computer boots and runs ifup scripts automatically via /etc/rc* scripts, you don't worry about it again until you have to reboot or your network goes down.)
Last edited by jhwilliams; 04-26-2009 at 08:20 AM.