This plugin lets you exclude categories from the standard blog posts query in WordPress

exclude-categories.php

<?php

/*
Plugin Name: Exclude Categories
Description: Adds a list of checkboxes on the reading settings page to explicitly exclude categories from the main blog listing.
Version: 0.1
Author: Robert O'Rourke
License: GPLv2 or later
*/

add_action( 'admin_init', 'exclude_categories' );
function exclude_categories() {
	add_settings_field( 'exclude_categories_id', __( 'Exclude categories from main blog' ), 'exclude_categories_field', 'reading' );
	register_setting( 'reading', 'exclude_categories_id', 'save_exclude_categories' );
}

function exclude_categories_field() {
	$exclude_categories = get_option( 'exclude_categories' ); ?>
	<input type="hidden" name="exclude_categories_id" value="" />
	<ul class="categorychecklist" style="max-height:220px;overflow:auto;"><?php
		$cats = get_terms( 'category', array( 'hide_empty' => false ) );
		foreach( $cats as $cat ) {
			$field_id = 'exclude_categories_' . $cat->term_id; ?>
		<li><label for="<?php echo $field_id; ?>">
			<input id="<?php echo $field_id; ?>" type="checkbox" <?php if ( $exclude_categories && in_array( "-{$cat->term_id}", $exclude_categories ) ) echo ' checked="checked"'; ?> name="exclude_categories[]" value="-<?php echo $cat->term_id; ?>" />
			<?php echo $cat->name; ?></label></li>
	<?php } ?>
	</ul>
	<?php
}

function save_exclude_categories() {
	if ( ! current_user_can( 'manage_options' ) )
		return false;

	if ( get_option( 'exclude_categories' ) )
		update_option( 'exclude_categories', $_POST[ 'exclude_categories' ] );
	else
		add_option( 'exclude_categories', $_POST[ 'exclude_categories' ] );
}

// if it's the home page and the main query then run our filter
add_action( 'pre_get_posts', 'exclude_categories_filter' );
function exclude_categories_filter( $query ) {
	global $wp_query;

	$exclude_categories = get_option( 'exclude_categories' );
	if ( $exclude_categories && $query->is_home && $query === $wp_query )
		$query->query_vars[ 'cat' ] = implode( ',', $exclude_categories );

	return $query;
}

?>