<?php the_category() ?>
<?php
wp_list_categories('orderby=name&include=3,5,9,16'); ?>

<?php foreach((get_the_category()) as $cat) {
if (!($cat->cat_ID=='37')) echo '<a href="' . get_bloginfo('url') . '/category/' . $cat->category_nicename . '/">'. $cat->cat_name . '</a>' . ', ';
} ?>

Hide / Exclude Categories From Posts Page

<?php if (is_front_page() && !is_paged() )
$posts = query_posts($query_string . '&cat=-35'); ?>

<?php
$cat_to_exclude = 35;
query_posts($query_string . '&cat=-'.$cat_to_exclude');
?>

<?php if (in_category('35')) continue; ?>
or


function exclude_category_home( $query ) {
if ( $query->is_home ) {
$query->set( 'cat', '-5, -34' );
}
return $query;
}

add_filter( 'pre_get_posts', 'exclude_category_home' );
Exclude Category from Homepage

Placing this code in your index.php file will cause your home page to display posts from all categories except category ID 3.

<?php
if (is_home()) {
query_posts("cat=-3");
}
?>
You can also add some more categories to the exclude-list(tested with WP 2.1.2):

<?php
if (is_home()) {
query_posts("cat=-1,-2,-3");
}
?>
or

function excludeCat($query) {
if ( $query->is_home ) {
$query->set('cat', '-3,-5,-23');
}
return $query;
}
add_filter('pre_get_posts', 'excludeCat');