Should a website have a search function?

Most websites have some sort of search function, but a non-trivial number don’t. Is this just an oversight by the designers, or are there good reasons for not providing search? Personally I hate websites without a search function, but then again, what I don’t know about UX would fill a great book.

I run a small, uncontroversial website which is frankly pretty primitive. We got a pro to redesign the site and I’m duly impressed with the result. However in his remake he removed the search function; communication is poor (I send polite emails, he does not reply) and I can’t find out why he removed it. Before I escalate matters to force communication I’d like to know what his reasons might have been.