Simple category and other archive page titles in WordPress 4.1+

prefixless_archive_titles.php

<?php

add_filter( 'get_the_archive_title', '{prefix}_cat_title' );
/**
 * Remove "Category: " prefix from Category archive pages
 */
function {prefix}_cat_title( $title ) {
    if( is_category() ) {
        $title = single_cat_title( '', false );
    }
    return $title;
}

add_filter( 'get_the_archive_title', '{prefix}_term_title' );
/**
 * Remove "Category: ", "Tag: ", and "{Taxonomy}: " prefixes from all term archive pages
 */
function {prefix}_term_title( $title ) {
    if( is_category() || is_tag() || is_tax() ) {
        $title = single_term_title( '', false );
    }
    return $title;
}