In a Graphical Session
When you're logged in graphically, you can run your graphical terminal emulator app as root, as others have said. The best way to do this is typically with gksu or gksudo, as this automatically handles changing HOME to /root and (less importantly) uses a temporary .Xauthority file (source). gksu is a frontend for both su and sudo and on most OSes will be configured to use whichever one is the more standard way for administrators to run programs as root. (Or you can specify which one with gksu --su-mode and gksu --sudo-mode, the latter of which is always equivalent to running gksudo without either flag.)
GNOME
gksu gnome-terminal or gksudo gnome-terminal
kdesu gnome-terminal or kdesudo gnome-terminal
- Please note that
kdesu is usually only present and in the PATH on systems where su is a supported way to run programs as root. That is not the case on some GNU/Linux OSes, such as Ubuntu.
Xfce
gksu xfce4-terminal or gksudo xfce4-terminal
LXDE
gksu lxterminal or gksudo lxterminal
As andcoz and aurelien lambrosse have said, running your graphical terminal emulator as root makes all the shells that come up in its tabs (and new windows, if created from the root terminal's menus) run as root.
In a Text-Based Session
If you don't have the ability to run GUI programs (virtual console login, ssh login without -X, or you just don't want to), the above solution won't work for you. In that case, you might consider using a screen manager that lets you control multiple terminals in one. This effectively achieves the same goal as a root-owned GUI terminal with multiple tabs...just without the GUI.
screen is the most common screen manager. You can use these commands to control it once it's running.
Or use byobu, a handy wrapper for screen. byobu is often not provided on non-Ubuntu systems (though it can be installed on them). But you indicated you're running ubuntu, so you should be able to use it.
byobu running on Ubuntu 11.10. Information about the current "window" and the system are shown at the bottom.
In byobu it's very easy to create new "windows" and to switch between them. F2 makes one, F3 switches backward, F4 switches forward, and F9 brings up the interactive main menu.
There are more default byobu keybindings. Here they are:
F2 Create a new window | F7 Scrollback and search
F3 Go to the prev window | F8 Rename a window
F4 Go to the next window | F9 Configuration
F5 Reload profile | F12 Screen escape sequence
F6 Detach from session | 'man byobu' - byobu's help
'byobu' - reattach session | 'man screen' - screen's help
Source: byobu built-in help, accessible in the F9 configuration menu
See also the documentation on the Ubuntu website for Screen (in the community wiki) and Byobu (in the Server Guide).