Kontra's article on Google, linking Android and Youtube via video search, speech recognition and phoneme harvesting, made a lot of sense, and I realised there's even more cleverness in that whole google product suite. I have Google Analytics on this site, and enjoy watching my bounce rate bounce and my visitors jump up and down and pages per visit and time on site and all this statistical goodness generally so much that I risk carpal tunnel from continuously hitting the refresh button on my permanently-open multiple analytics tabs in firefox.
I don't know why Analytics is free, but here's a possible reason: when google sends a visitor to your site from a search result, the only way they can judge the quality of that result (the relevance of your site to the search query), without analytics, is whether and how soon the user clicks on another result for the same search. Now that you have analytics installed, they have much richer and deeper information: how long does the user stay on your site, how many and which pages to they visit? Having this information allows them decide whether that particular result was in fact a "good" hit.
I have no idea if google correlates search data with analytics data. But the point is, they have the data. And if I were google, I would do it. Wouldn't you? It's not necessarily a Bad Thing, but it's nice to know what you're paying for when it's free.