You clearly want to tell the user that the item(s) sought for are not available, Jared says. Instead, most search pages often produce a list of random results, none of which complete the user’s quest. When you decide to present possibly related items, make sure they are relevant for the user’s task.

Also, don’t make the mistake made by Best Buy, when they show products on the result page that are actually sold out (which you find out only when you move to the individual product pages).

Spellchecking should be included, in case of mispelled search terms (pun intended). A simple “did you mean” link may be all you need.

Best Bets could also be useful, based on what’s popular or in frequent demand. It’s a fair chance that the unlucky searcher may be looking for the same thing other visitors are looking for. How about popular search terms? Or recent terms, for that matter?

You can also guide the unlucky searcher to the site navigation, I think. Browsing may be a better strategy if you have no clue of what to search for.

Can you think of other zero hit search result strategies?

Regarding patterns, have a look at:
http://patterntap.com/tap/collection/search
http://patterntap.com/tap/collection/404-pages

There should be a pattern for “search returned 0 hits”, as there are numerous ways of providing something of more use than an empty page.