Function: wp_get_attachment_metadata

If you need quick access to the image dimensions from the Media Library, this will add a ‘Dimensions’ column

add_filter( 'manage_media_columns', 'add_media_columns');
function add_media_columns( $columns ) {
    $columns['dimensions'] = 'Dimensions';
    return $columns;
}
add_action( 'manage_media_custom_column', 'fill_media_columns', 10, 2 );
function fill_media_columns( $column_name, $id ) {
    switch ( $column_name ) {
        case 'dimensions' :
            $meta = wp_get_attachment_metadata( $id );
            if ( isset( $meta['width'] ) ) {
                echo $meta['width'].' x '.$meta['height'];
            }
        break;
    }
}

Don’t forget to prefix these to avoid clashes with other code!