[WordPress] Mini plugin to exclude any given categories from queries and widgets. The first file is not part of the plugin, but is included to demonstrate the differences in applying $query->set() instead its wrapper function set_query_var().

exclude-categories-from-ajacent-posts.php

<?php
/**
 * Exclude categories from prev/next post links.
 *
 * $exclude  (array) - category slugs to retrieve IDs from
 * $excluded (array) - category IDs to be excluded
 */
$exclude  = array();
$excluded = array();

// Mini plugin active?
if( function_exists( 'glckprss_exclude_categories__category_names' ) ) {
	
	$exclude = glckprss_exclude_categories__category_names();
	
else {
	
	$exclude  = array(
		get_category_by_slug( 'my-category' ),
		get_category_by_slug( 'my-other-category' )
	);
}

// Retrieve IDs
foreach( $exclude as $category ) {

	if( $category )
		$excluded[] = absint( $category->term_id );
}

/* Next Post */
next_post_link( '%link', '%title', false, $excluded );

/* Previous post */
previous_post_link( '%link', '%title', false, $excluded );

exclude-categories.php

<?php 

/**
 * Does NOT apply to the Recent Posts widget. 
 */
function glck1403271109_exclude_categories( $query ) {

	$excluded = array( '1', '2' );

	if( ! is_admin() )
		set_query_var( 'category__not_in', $excluded );
}
add_filter( 'pre_get_posts', 'glck1403271109_exclude_categories' );


/**
 * Does apply to the Recent Posts widget. 
 */
function glck1403271122_exclude_categories( $query ) {

	$excluded = array( '1', '2' );

	if( ! is_admin() )
		$query->set( 'category__not_in', $excluded );
}
add_filter( 'pre_get_posts', 'glck1403271122_exclude_categories' );

glckprss-exclude-categories.php

<?php
/**
 * Plugin Name: Mini Plugin: Exclude Categories
 * Description: Exclude categories from WordPress queries and widgets.
 * Version: 2014.02
 * Author: Caspar Hübinger
 * Author URI: http://glueckpress.com/
 * License: GNU General Public License v2 or later
 * License URI: http://www.gnu.org/licenses/gpl-2.0.html
 */

if ( ! defined( 'ABSPATH' ) )
	exit;


/**
 * Configuration: category names to be excluded.
 */
function glckprss_exclude_categories__category_names() {

	return array(
		'my-category',
		'my-other-category',
	);
}


/**
 * Load plugin.
 */
function glckprss_exclude_categories() {

	// Exclude categories.
	add_filter(
		'pre_get_posts', // …from main query
		'glckprss_exclude_categories__exclude_query_categories'
	);
	add_filter(
		'widget_categories_args', // …from category widget
		'glckprss_exclude_categories__exclude_widget_categories'
	);
	add_filter(
		'widget_categories_dropdown_args', // …from dropdown category widget
		'glckprss_exclude_categories__exclude_widget_categories'
	);
}
add_action( 'plugins_loaded', 'glckprss_exclude_categories' );


/**
 * Get IDs for categories to be excluded.
 *
 */
function glckprss_exclude_categories__excluded_categories() {

	// Category names to be excluded.
	$names = glckprss_exclude_categories__category_names();

	$excluded = array();

	foreach( $names as $name ) {

		$ob         = get_category_by_slug( $name );
		$id         = $ob ? absint( $ob->term_id ) : '';
		$excluded[] = $id;
	}

	return $excluded;
}


/**
 * Exclude categories from queries.
 *
 */
function glckprss_exclude_categories__exclude_query_categories( $query ) {

	$excluded = glckprss_exclude_categories__excluded_categories();

	if( ! is_admin() )
		$query->set( 'category__not_in', $excluded );
}


/**
 * Exclude categories from category widget.
 *
 */
function glckprss_exclude_categories__exclude_widget_categories( $args ){

	$excluded = glckprss_exclude_categories__excluded_categories();
	$args[ 'exclude' ] = $excluded ? $excluded : '';

	return $args;
}