Is there a safer and better Google?

I'm a bit paranoid but I really dislike having every byte I type stored on their servers indefinitely and since Google is pretty much a monopoly now it's entirely possible that they are controlling some information (other than for ads revenue).

So is there a better Google?

It might not be a search engine.

Perhaps just a forum with links you won't find on Google search or anywhere else.

http://www.eff.org/deeplinks/2009/09/what-information-personally-identifiable
A very small amount of information can be used to identify you uniquely among millions. With all the data you've typed into search engines over the years, social engineering becomes alarmingly easy.

You can often identify someone's gender from their search history, or even from web pages they've visited: http://www.mikeonads.com/2008/07/13/using-your-browser-url-history-estimate-gender/
You can get their general location from their IP address, and often also from their search terms alone. For example, have you ever looked up local movie theaters or searched for restaurant reviews? Maybe you've looked for the dates a band was playing at a nearby venue.

If you can identify who someone is, and armed with that person's search history, you can "prove" that you knew them: "Hey, John, you remember me? You were talking about building that embedded system, maybe seven months ago, I suggested getting a Beagleboard, how'd that work out?" (Suppose you noticed that they were searching for general terms one week, and then searching for more specific terms like "beagleboard price" the next. You might even take a shot in the dark and say you met him at a local restaurant, as chances are he won't remember whether or not he dined out on a specific day seven months ago.