At the heels of Google and Yahoo, and Bing's tests, Yandex, the largest Russian search engine has dropped out all search query data from the referrer. That means, Yandex has gone 100% not provided.
So not only will you not get your search query data from Google and Yahoo searches but also you won't be getting them from your favorite Russian search engine. I should add, Bing is testing it now as well.
You can read the announcement in Russian if you like. It translates to:
In December last year we started an experiment to encrypt text query in the Referer , which gradually expanded. By February, the share encrypted data has reached 30% of user requests. Time that has passed since the announcement, made it possible for webmasters to shift to other methods of estimating the user's interests. From today we start encrypting referrers at 100% of the flow of requests. Statistics searches for sites in your metrics and service for webmasters still available in full.
I tested this myself and the interesting part is Yandex does not go over SSL. So it isn't all that secure.
Try it, a search for [what is my referrer] at least on Yandex.ru from New York go over http and not https. But if you click through to the first result, you will clearly see that they are specifically removing the search query data. Is that making it secure? Not 100% because it is not over SSL. But it is removing that data from analytics packages.
Forum discussion at Yandex Forums.