How to hide a post from ‘Recent Posts’ widget?

You can exclude posts from the recent posts widget via the widget_posts_args filter:

add_filter( 'widget_posts_args', 'exclude_posts_wpse_103570');

function exclude_posts_wpse_103570( $args ){
    // post ID's to exclude:
    $args['post__not_in'] = array( 123, 234, 345 );
    return $args;
}