I found following description in a book, "Search Patterns: Design for Discovery", which I bought from O'Reilly Japan (Japanese Edition).
A solid taxonomy with clear categories and labels is enough. Perhaps a sitemap or index is useful to complement navigation, but search is unnecessary. In fact, adding search may be downright dangerous, since most queries will lead to nowhere.
In this site, I put search box to search within the site, but I think the description above is right. At most case, search result contains nothing. I use search box with appropriate words, because I know contents of this site. But visitors can't put good words for search.
Most of visitors come some page of this site, and think what's this site? then use search box without knowledge of this site. Not always enter at top page of this site.
Considering about this, I changed settings of Google Custom Search to search from whole WEBs with priority of this site.
It should be better than no search results.