When Google made their mistake with Street View cars, they made to to point out how serious they take privacy. In that blog post, Google's Alan Eustace, Senior VP, Engineering & Research said:
Next week we will start offering an encrypted version of Google Search.
Right now, if you go to https://www.google.com/ you are redirected to the non https version, http. Even if you try appending a, https://www.google.com/search?q=google, to a query you, are redirected back to the main non-secure Google search.
This may change according to Google's own words. Exactly how Google will release "an encrypted version of Google Search" is not clear. But it should launch this week, according to that post.
Forum discussion at WebmasterWorld.

Comments:
Luke Jones
05/17/2010 01:42 pm
I can't really see how this will be beneficial to anyone. It's just people scaremongering because of what happened recently with the Street View problem. We've been searching for twelve years without this - why start now?
TOMHTML
05/17/2010 02:27 pm
It will be a big problem fom webmasters as the referer is not available when a visitor comes from a secure page... You will no longer be able to track users' keywords in Google Analytics
Allen
05/18/2010 07:04 am
I read somewhere(reliable) that Google apologizes collecting personal data! I don't think Google will make it by default to all users instead this new offer would be available as an option to those who want to explore more things, say for professionals!