I will very quickly stop using a given website if it doesn't provide a good, on-site search. If I'm looking for information that I know exists on a particular website, I see no reason to involve a third-party search engine in the equation at all.

Granted, a lot of sites out there that provide a search function do not necessarily need one, and would instead benefit from an organized, hierarchial index. With these types of websites, using the search function only adds unnecessary friction.