single_cat_slug()?

I use this in one of my themes (in the category.php template):

<?php /* used to create dynamic category link */
$curr_cat = single_cat_title( '', false );
$cat_id = get_cat_ID( $curr_cat );
$category_link = get_category_link ( $cat_id );
?>

You could probably strip out the category slug from the end of the ‘$category_link’ if you need the slug only.

another possibility:

<?php $cat = get_term_by('name', single_cat_title('',false), 'category'); echo $cat->slug; ?>

http://codex.wordpress.org/Function_Reference/get_term_by