Is it possible to remove the default terminal and replace it with some other terminal (like terminator or terminology)?

I wouldn't remove it. Given it is the default terminal emulator for the Unity/Gnome desktop environment, there could be some obscure program/script that use it unconditionally and you'll have an error (probably two years from now when you didn't remember what can have caused it).

The preferred way is:

1. Install the new terminal emulator, for example

   sudo apt-get install terminator
   

2. Set the update-alternative method to choose it:

   [romano:~/tmp] % sudo update-alternatives --config x-terminal-emulator
   There are 8 choices for the alternative x-terminal-emulator (providing /usr/bin/x-terminal-emulator).
   
     Selection    Path                             Priority   Status
   ------------------------------------------------------------
   * 0            /usr/bin/terminator               50        auto mode
     1            /usr/bin/gnome-terminal.wrapper   40        manual mode
     2            /usr/bin/koi8rxterm               20        manual mode
     3            /usr/bin/lxterm                   30        manual mode
     4            /usr/bin/rxvt-xpm                 8         manual mode
     5            /usr/bin/rxvt-xterm               10        manual mode
     6            /usr/bin/terminator               50        manual mode
     7            /usr/bin/uxterm                   20        manual mode
     8            /usr/bin/xterm                    20        manual mode
   
   Press enter to keep the current choice[*], or type selection number:
   

...and that should be it. If you have probelms, you can look here: How can I set default terminal used in Unity?

Notice however that there is a bug/misfeature of the underlying library that makes that all the things that use the "open in terminal" will not respect the selection above. The bug was reported and acknowledged in 2010, there is a patch available, but it's still here. I wouldn't hold my breath for a fix.

A system-wide workaround could be to remove the gnome-terminal binary and replace it with a link to x-terminal-emulator --- should work most of the time...

Alternatively, you you have in your PATH the $HOME/bin directory before /usr/bin (as everyone has, I suppose) you can simply ln -s /usr/bin/terminator $HOME/bin/ (no privileges required) and glib will happily use the link instead of the real gnome-terminal.