First, you have something contradictory in your question. You said, "it started to show user@hostname: ~/currentdir in its title, changing it whenever I cd to another directory", but the image attached said something else. I am almost sure that if you've selected "Replace initial title" setting in gnome-terminal's preferences and if you use this ~/.bashrc file as you said, your terminal should look like in the following image:

Second, you're totally wrong with: "vim, for example, sets current filename as a title". To do this, you must to heve a file named .vimrc in your home directory with the following code inside:

let &titlestring = $USER . "@" . hostname() . ": vim " . expand("%:t")
if &term == "screen"
  set t_ts=^[k
  set t_fs=^[\
endif
if &term == "screen" || &term == "xterm"
  set title
endif

And one more thing: I don't understand yet exactly for what do you using that if from the 11th line until 40th line in your .bashrc file, but setting up TERM="gnome-256color" at the line 33 may be a problem in this case. So, I suggest you to comment that line, or to remove all the code between lines 11 and 40.

After all of this done, when you will use vim, your terminal should look like:

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.