DuckDuckGo
InternetThree months ago, I switched to using DuckDuckGo as my primary search engine. So far, I've been quite happy at how well it's worked, and now I couldn't imagine going back to Altavista Lycos Excite LookSmart Northern Light Google.
(Rubenerd's site search, has also been served by DDG for a couple of years).
The web is littered with examples of services that based their existance on not being something else. Ello and ADN weren't Twitter. Diaspora and Google+ weren't Facebook. Few of them had/have stuck, largely because push factors alone aren't sufficient to sway changes in behaviour.
DuckDuckGo is indispensible because of pull factors. Aside from not being Google (increasingly a plus in my book), it has has features Google doesn't have, and I can't live without them now.
Take bang operators. Casey Liss did a great writeup of these, but in a nutshell they allow you to prepend tags to search queries to take you elsewhere. Typing the following will take you to Wikipedia's Bakemonogatari article:
bakemonogatari !w
For when DDG's results aren't enough (increasingly rare), you can even do a secured Google search which won't leak referrer information:
bakemonogatari !g
Answers are also a helpful addition. For example, if you search for regex, you'll get a summary of all the operators. Popular responses from the Stack Exchange network also appear inline, often saving a click.
If you disable JavaScript for security or otherwise, there's also a secure HTML-only alternative that has the advantage of loading much quicker. Remember when every site didn't load JS libraries and fonts that could rival operating systems of yore in size in time to load?
If you're interested, have a go at setting it as your defauly search engine for a few days (instructions for Firefox, Safari, and Chrome). You may be surprised.
