If you want to run programs without using Terminal, I can deduce that you mean only GUI programs. And each one from all these GUI applications have in general an .desktop file located in /usr/share/applications/ or in your user directory ~/.local/share/applications. So to start a program as root you must to edit or better duplicate its associated .desktop file.

Let's take for example Gedit, the default GUI editor in Ubuntu. Its .desktop file is /usr/share/applications/gedit.desktop and has the following content:

[Desktop Entry]

Name=gedit

GenericName=Text Editor

Comment=Edit text files

Exec=gedit %U

Terminal=false

Type=Application

StartupNotify=true

MimeType=text/plain;

Icon=accessories-text-editor

Categories=GNOME;GTK;Utility;TextEditor;

X-GNOME-DocPath=gedit/gedit.xml

X-GNOME-FullName=Text Editor

X-GNOME-Bugzilla-Bugzilla=GNOME

X-GNOME-Bugzilla-Product=gedit

X-GNOME-Bugzilla-Component=general

X-GNOME-Bugzilla-Version=3.10.4

X-GNOME-Bugzilla-ExtraInfoScript=/usr/share/gedit/gedit-bugreport

Actions=Window;Document;

Keywords=Text;Editor;Plaintext;Write;

X-Ubuntu-Gettext-Domain=gedit



[Desktop Action Window]

Name=Open a New Window

Exec=gedit --new-window

OnlyShowIn=Unity;



[Desktop Action Document]

Name=Open a New Document

Exec=gedit --new-document

OnlyShowIn=Unity;

Now create a duplicate of this file as follow:

sudo cp /usr/share/applications/gedit.desktop /usr/share/applications/root_gedit.desktop

and make the following changes:

[Desktop Entry]

Name=gedit as root

GenericName=Text Editor as root

Comment=Edit text files

Exec=gksudo gedit %U

Terminal=false

Type=Application

StartupNotify=true

MimeType=text/plain;

Icon=accessories-text-editor

Categories=GNOME;GTK;Utility;TextEditor;

X-GNOME-DocPath=gedit/gedit.xml

X-GNOME-FullName=Text Editor

X-GNOME-Bugzilla-Bugzilla=GNOME

X-GNOME-Bugzilla-Product=gedit

X-GNOME-Bugzilla-Component=general

X-GNOME-Bugzilla-Version=3.10.4

X-GNOME-Bugzilla-ExtraInfoScript=/usr/share/gedit/gedit-bugreport

Actions=Window;Document;

Keywords=Text;Editor;Plaintext;Write;

X-Ubuntu-Gettext-Domain=gedit



[Desktop Action Window]

Name=Open a New Window

Exec=gksudo gedit --new-window

OnlyShowIn=Unity;



[Desktop Action Document]

Name=Open a New Document

Exec=gksudo gedit --new-document

OnlyShowIn=Unity;

After this, when you will search for gedit in the Dash you will see two instances of gedit: one named Text Editor and one Text Editor as root. You should open that one named Text Editor as root if you want to run gedit as root.

Note: gksudo must to be installed in order to use it. If you don't have installed, you can install it from terminal using:

sudo apt-get install gksudo