Facebook Search is surely the most widely used function of the website. I myself have facebook set to be my homepage, therefore it's handier to just type anything I want in there - rather than having to visit google first.
What do you generally search for, and how can Facebook serve you relevant hits?
Actually, you can get web search results on Facebook through Bing. It is one of the side tabs on the search page. But I can't imagine many people doing that.