Amazing how many people just slap a keyword search interface on their site and call it a day... They'd be better off pointing at Google rather than rolling a crappy home grown solution.
Good post explaining table stakes for reasoning about whether your site search works (and measuring whether changes make it work better).
If anyone is interested in having this but not rolling their own, www.switfype.com (ycombinator 2012) provide a pretty powerful site (and mobile app, etc) search solution, which includes these kinds of analytics and more (disclaimer: the founders were my roommates :-)).
Constructor.io founder here. Swiftype does a great job of being pretty good at a lot of things. Constructor.io focuses on state-of-the-art in autocomplete. Looking at one of the websites Swiftype advertises powering like www.bulbamerica.com, you can see they miss basic misspellings.
Constructor.io, aside from providing typo-tolerance as you type, also optimizes autocomplete rankings to prioritize results most likely to lead to conversions, provides search suggestions as well as product suggestions, and much more.
If you want a pretty good full search solution, use swiftype. If you want to add the best state-of-the-art autocomplete that's proven to increase conversions, get in touch with us at constructor.io :)