What's the equivalent of the "cls" command from Windows/DOS?

You can use reset. This resets the whole terminal, so that may be a bit overkill though.

Note on Konsole:
@Mechanical snail noticed "in Konsole 4.8.5, the old text is still there if you scroll up". @gertvdijk explained that it is "a feature. There's Ctrl+Shift+K for Konsole (reset and clear scrollback)."

Add this line to ~/.bashrc (i.e., the file called .bashrc, located in your home folder -- you can see it in Nautilus by pressing Ctrl+H):

alias cls='printf "\033c"'

Now the cls command will clear the screen like in Windows. It will put you back to the top of a Terminal window, with no text shown above it. (It will not delete the shell's command history.)

This works because:

• .bashrc runs every time a bash shell starts up.
• The alias command defines the cls command to run the command quoted on the right-hand side.
• printf command writes characters to the terminal. It accepts escape codes. The octal 033 is the character used to signal the beginning of a terminal control code. The control code c tells the terminal to clear itself.
• So, with this modification to .bashrc. running cls sends the necessary data to the terminal to tell it to clear itself.

In your current terminal window, just type the following:

printf "\033c"