Spawn new terminal window with the same directory as the previous window

In the menu of Gnome-terminal, use:

File --> Open Terminal 

That will open a new window using the pwd as the directory.

Also, you may set the open tabs:

Edit --> Preferences --> General --> Open new terminals in: --> select tab.

So new terminals will open in the same window with the same pwd.
You will still be able to open new windows if needed:

Alt-F2 --> gnome-terminal

On Arch Linux + GNOME (at least), you can add the following line into ~/.bashrc to have new Terminal windows opened in the current directory:

source /etc/profile.d/vte.sh

There is already a related question about new tabs. It turns out that the answer is the same for new windows.