Permanently disable color in default terminal

In your .bashrc file, you'll find lines

# uncomment for a colored prompt, if the terminal has the capability; turned
# off by default to not distract the user: the focus in a terminal window
# should be on the output of commands, not on the prompt
force_color_prompt=yes

Put a # comment sign in front of force_color_prompt=yes line and restart terminal. After the change, the line should be

#force_color_prompt=yes

Edit: This will turn of the color from terminal. But if some programs has color support built-in in them and if you want to turn them off too, follow @Zanna's answer. Basically you need to comment out the lines like alias ls='ls --color=auto' etc.

If you have set a coloured prompt see @Anwar's answer

The colours from the output of commands such as ls are made by aliases.

To disable this, find and comment out (by inserting # at the start of the line) these lines in your ~/.bashrc

alias egrep='egrep --color=auto'
alias fgrep='fgrep --color=auto'
alias grep='grep --color=auto'
alias ls='ls --color=auto'

when done, source ~/.bashrc to get the immediate effect or just close the terminal and open a new one