While most people have a search box for their blogs, so people can look up previous topics etc, I just came across Lijit and have added that in my sidebar of this blog.
Here's what it looks like:
It seems to perform all the usual search functions for the searcher that other search boxes do, but the advantage is that it provides valuable information back to you, the blogger, on what people have searched for and found - but also what keywords they searched for and didn't find any links/results.
Both are useful when you come to write future blog posts, as maybe you can choose to address some of topics that people searched for and didn't find links to, and also you can keep talking about the most searched about topics!
Sample search: 4 pages of results
I only put it on my blog last night but already I can see that my top referring search location is Delhi! Lijit sends you a weekly email showing your stats which is great - or else you can log into the website www.lijit.com and enter your name and password and all search information shows up for you.
In addition to using this to search your blog, you can also set it up to search your social networks too - including linkedin, twitter, Flickr,Digg, Reddit....and also include other people's blogs as well.
It's free, easy to set up, and I think it's going to be useful feedback - and different from what you get from google analytics. Give it a try and let me know what you think.