Integrate with statistics, i.e. 'Top Searches'

This doesn't need to be in the Search API module, and, in my opinion, also shouldn't. While only a part of the users will want such a feature, it would cost performance and memory for all others, too.
With hook_search_api_query_alter() you have a very easy way to react upon search queries, and store whatever data in whichever way you want.
Just create a custom module for it, this could be valuable to a lot of Search API users. I'd then just link to it from the Search API project page (although the list now starts to grow a bit out of control …).

Here you go http://drupal.org/project/search_api_stats

A bit late maybe, but I've now included it in the list.
Sorry, must have slipped me by originally.