You can configure sudo to never ask for your password.
Open a Terminal window and type:
sudo visudo
In the bottom of the file, add the following line:
$USER ALL=(ALL) NOPASSWD: ALL
Where $USER is your username on your system. Save and close the sudoers file (if you haven't changed your default terminal editor (you'll know if you have), press Ctl + x to exit nano and it'll prompt you to save).
As of Ubuntu 19.04, the file should now look something like
#
# This file MUST be edited with the 'visudo' command as root.
Defaults env_reset
Defaults mail_badpass
Defaults secure_path="/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/snap/bin"
root ALL=(ALL:ALL) ALL
%admin ALL=(ALL) ALL
%sudo ALL=(ALL:ALL) ALL
YOUR_USERNAME_HERE ALL=(ALL) NOPASSWD: ALL