Ubuntu – Standard accounts are able to get root access using sudo without password request

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.
#
# Please consider adding local content in /etc/sudoers.d/ instead of
# directly modifying this file.
#
# See the man page for details on how to write a sudoers file.
#
Defaults    env_reset
Defaults    mail_badpass
Defaults    secure_path="/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/snap/bin"

# Host alias specification

# User alias specification

# Cmnd alias specification

# User privilege specification
root    ALL=(ALL:ALL) ALL

# Members of the admin group may gain root privileges
%admin ALL=(ALL) ALL

# Allow members of group sudo to execute any command
%sudo   ALL=(ALL:ALL) ALL

# See sudoers(5) for more information on "#include" directives:

#includedir /etc/sudoers.d

YOUR_USERNAME_HERE ALL=(ALL) NOPASSWD: ALL

After this you can type sudo <whatever you want> in a Terminal window without being prompted for the password.

This only applies, to using the sudo command in the terminal. You'll still be prompted for your password if you (for example) try to install a package from the software center

This behavior is controlled by PolicyKit's LocalAuthority configuration. From the ADMINISTRATOR AUTHENTICATION section of man pklocalauthority:

   By default, "administrator authentication" is defined as asking for the
   root password. Since some systems, for usability reasons, don't have a
   root password and instead rely on a group of users being member of an
   administrative group that gives them super-user privileges, the Local
   Authority can be configured to support this use-case as well.

   Configuration for the Local Authority is read from files in the
   /etc/polkit-1/localauthority.conf.d directory. All files are read in
   lexigraphical order (using the C locale) meaning that later files can
   override earlier ones. The file 50-localauthority.conf contains the
   settings provided by the OS vendor. Users and 3rd party packages can
   drop configuration files with a priority higher than 60 to change the
   defaults.

At least in my (18.04) Ubuntu system, the two relevant files are 50-localauthority.conf and 51-ubuntu-admin.conf:

$ head /etc/polkit-1/localauthority.conf.d/*
==> /etc/polkit-1/localauthority.conf.d/50-localauthority.conf <==
# Configuration file for the PolicyKit Local Authority.
#
# DO NOT EDIT THIS FILE, it will be overwritten on update.
#
# See the pklocalauthority(8) man page for more information
# about configuring the Local Authority.
#

[Configuration]
AdminIdentities=unix-user:0

==> /etc/polkit-1/localauthority.conf.d/51-ubuntu-admin.conf <==
[Configuration]
AdminIdentities=unix-group:sudo;unix-group:admin

So, in order to revert to the PolicyKit default, which uses AdminIdentities=unix-user:0 (i.e. root) instead of the Ubuntu default AdminIdentities=unix-group:sudo;unix-group:admin (i.e. members of sudo and/or admin groups), it's sufficient to either rename the 51-ubuntu-admin.conf file so that it is loaded earlier or not at all - for example

sudo mv /etc/polkit-1/localauthority.conf.d/51-ubuntu-admin.conf{,.ignore}

or comment out the AdminIdentities entry therein. The former option is perhaps cleaner and more maintainable.