Thanks for the tip, Shan.
For anyone interested, this is how I turned off the breadcrumbs on the store homepage only: In the /customer/home.tpl file, replace this line...
Code:
{include file="location.tpl"}
...with these lines...
Code:
{if $main ne "catalog" or $current_category.category ne ""}
{include file="location.tpl"}
{/if}
Now the breadcrumb navigation links appear on all pages except for the Store homepage.