Are you concerned about search privacy? If so, then you might be interested in two smaller search engines. Google and Bing, the leading competitors in search, store your search data for up to 18 months. But Blekko and DuckDuckGo are banking on you wanting more privacy than that.
Blekko - Blekko stores your search data for 48 hours, and that's it. But the problem with Blekko is that your searches are confined only to sites that you or your friends tell it to search. The search engine makes use of "slashtags," which are akin to Twitter's hashtags. The intent is to cut out spam and undesired results from your searches. This type of search engine can be useful to your business if you can train your customers to use it and add important search terms related to your website as slashtags for their searches. Good luck in that.
DuckDuckGo - DuckDuckGo is more traditional in that they do crawl the Web and return search results based on keyword-related queries. And they do not collect your private information at all. Nada. You can also turn the privacy features off, if you prefer.
DuckDuckGo even refers you to two other search engines (on its privacy page) that do not collect your private information: Ixquick and Scroogle. The latter seems to base its results on Google search results, but it appears to be the only one of the four sites mentioned in this post to do so.
Are these smaller search engines good? Can they be good for your business? You'll have to test them. I ran a test at both Blekko and DuckDuckGo. I was impressed that SBM was No. 1 at DuckDuckGo for the search phrase "small business marketing minnesota." Of course, I'm No. 1 in both Google and Bing for the same phrase.
If you train your customers to conduct private searches at these search engines when searching for your business or services that you offer, then you might get some traffic from these sources.