Getting the Next and Previous Posts Titles in the Sidebar?

The existing WordPress functions are only for displaying one previous or next post. I quickly wrote functions to display any number of posts.

Paste the following in your theme functions.php file:

function custom_get_adjacent_posts( $in_same_cat = false, $previous = true, $limit = 2 ) {
    global $post, $wpdb;

    $op = $previous ? '<' : '>';

    if ( $in_same_cat ) {
        $cat_array = wp_get_object_terms($post->ID, 'category', array('fields' => 'ids'));

        $join = " INNER JOIN $wpdb->term_relationships AS tr ON p.ID = tr.object_id INNER JOIN $wpdb->term_taxonomy tt ON tr.term_taxonomy_id = tt.term_taxonomy_id AND tt.taxonomy = 'category' AND tt.term_id IN (" . implode(',', $cat_array) . ")";
    }

    $posts = $wpdb->get_results( $wpdb->prepare( "SELECT p.* FROM wp_posts AS p $join WHERE p.post_date $op '%s' AND p.post_type="post" AND p.post_status="publish" ORDER BY p.post_date DESC LIMIT $limit", $post->post_date, $post->post_type ) );

    return $posts;
}

function custom_adjacent_posts_links( $in_same_cat = false, $previous = true, $limit = 2 ) {
    $prev_posts = custom_get_adjacent_posts( $in_same_cat, $previous, $limit );
    if( !empty($prev_posts) ) {
        echo ($previous) ? '<h3>Previous Posts:</h3>' : '<h3>Next Posts:</h3>';
        echo '<ul>';
        foreach( $prev_posts as $prev_post ) {
            $title = apply_filters('the_title', $prev_post->post_title, $prev_post->ID);
            echo '<li><a href="' . get_permalink( $prev_post ) . '">' .$title . '</a></li>';
        }
        echo '</ul>';
    }
}

In your sidebar file, where you want to display the posts, use custom_adjacent_posts_links( true ); to display the two previous posts in the same category and custom_adjacent_posts_links( true, false ); to display the next two posts in the same category.