aaronk, for Elgg 1.8 I would look at the ways to manipulate the filter menus in particular, especially the prepare plugin hook and the elgg_unregister_menu_item() function.

Steve, I saw the elgg_unregister_menu_item() function mentioned in another discussion as well --thanks for the tip, every bit will help...

For kicks.  A quick little invisiblity cloak for CSS friendly browsers:

ul.profile-action-menu li:first-child { display: none; }
li.elgg-menu-item-friend { display: none; }
select.elgg-input-dropdown option:nth-of-type(2) { display: none; }
#elgg-widget-type-friends { display: none; }

No more friends (assuming there weren't any to begin with).