Automatically login to WordPress, with a given user and optionally whitelist IPs. Add this to the bottom of wp-config.php, or your theme functions.php. To automatically login, visit the admin login page (/wp-login.php or /wp-admin/).

wp-auto-login.php

/**
 * Automatically logs in a visitor when accessing the admin login area (/wp-login.php)
 *
 * @copyright Copyright (c) 2014, Jackson Cooper
 * @license MIT
 *
 * Whitelist IPs: add IPs to whitelist in $ip_whitelist. If it is empty, it will allow all IPs.
 * Username: Specify the username to login as with the "user" GET parameter (eg. ?user=admin).
 *           If the "user" get parameter is not set, $default_user_login will be used. If set
 *           to "*", it will login as the first administrator found. Otherwise it will use the
 *           value set.
 *
 * @note If already logged in, or just logged out, it will do nothing.
 */
function automatic_user_login() {

    // Already logged in, not necessary
    if (is_user_logged_in()) {
        wp_redirect(admin_url());
        return;
    }

    // IP whitelist. If this is empty, whitelisting will be disabled.
    $ip_whitelist = array('127.0.0.1', '::1');

    // Default user to login as.
    // If this is "*", the first administrator user will be used.
    // If the "user" GET parameter is set, this will be used.
    $default_user_login = '*';

    $ip_blocked = (!empty($ip_whitelist) and !in_array($_SERVER['REMOTE_ADDR'], $ip_whitelist));
    $user_logged_out = (isset($_GET['loggedout']) and $_GET['loggedout'] === 'true');
    if (($ip_blocked)          // IP not whitelisted
        or ($user_logged_out)) { // User just logged out
            return;
    }

    // Fetch the user to login as, if it exists
    $user_login = (isset($_GET['user'])) ? $_GET['user'] : $default_user_login;
    if ($user_login === '*') {
        $user = current(get_users(array('role' => 'administrator')));
        if ($user === false) wp_die(__( 'ERROR: No admin users exist.'));
    } else {
        $user = get_user_by('login', $user_login);
        if ($user === false) {
            $admin_users = get_users(array('role' => 'administrator'));
            $admin_users_atr = implode(', ', array_map(function($admin_user) {
                return $admin_user->data->user_login;
            }, $admin_users));

            wp_die(__("ERROR: User '$user_login' does not exist. Other administrators: $admin_users_atr"));
        }
    }

    // Login as $user and re-load / re-direct to the admin page
    $user_id = $user->ID;
    wp_set_current_user($user_id, $user->user_login);
    wp_set_auth_cookie($user_id, true);
    do_action('wp_login', $user->user_login);
    wp_redirect(admin_url());
}
add_action('login_init', 'automatic_user_login');