43 Alternative Web Search Engines 
If you think there are only 3 or 4 search engines in Internet you'll be surprised at how many different Google alternatives are available.
Even if you discard specialized search engines, web directories and price comparison websites you'll easily end up with hundreds of websites in the list. For this article I've only included the general purpose search engines.
This is the alphabetically ordered list of generic search engines that have their own web crawler :
Active Search Results was launched in 2009 and it's an independent search engine that uses a patented ranking algorithm called ASR Ranking. This algorithm is based in user activities in the ASR website and it ranks the websites according to the points given to the users who submitted each website to ASR.
Baidu is an Chinese-American company established in 2000 and the web search is its main product. Baidu also includes an Image Search service, a social media platform called Baidu PostBar, a document sharing platform called Baidu WenKu, an encyclopedia and many other services.
Bing was previously known as MSN Search and it was launched in 2009 by Microsoft. It's the default search engine in Internet Explorer and Edge.
Cốc Cốc is a search engine made by a Vietnamese company with the same name. It was created to handle the complexities if the Vietnamese language better than other search engines.
Daum is a very popular South Korean web portal lauched in 1997 that includes a search engine service.
DuckDuckGo was launched in 2008 and it gets the search results from about 50 sources like Wikipedia and other search engines. DuckDuckGo respects the user's privacy.
EntireWeb was launched in 2000 by a Swedish company called Entireweb Sweden AB, which is a supplier of search technology solutions for other search engines.
Exalead is a French company founded in 2000 that provides search-based applications.
ExploraTodo is the first independent search engine made in Latin America. It was launched in 2014 in Chile and its main feature is the total respect of privacy. ExploraTodo donates part of its revenue to a non-profit organization called Samuel Aun Weor to help those in need.
Gibiru was founded in 2009 and it provides private, uncensored and anonymous search results.
Gigablast was launched in 2000 by Matt Wells and it's the source of search results for several search engines.
Haosou is the new name for the www.so.com search engine. Haosou is a property of Qihoo 360, a Chinese internet security company. Haosou can search text, images, music, maps and videos.
Iskanie is a Russian search engine and their name means searching. Iskanie's goal is to index websites written in Russian and Ukranian languages.
Istella was launched in 2013 and it's the search engine for the Italian web. Istella can search text, images, maps, news and videos.
Izsearch is a general purpose search engine that includes thematic search covering over 50 popular topics. Izsearch doesn't collect personal information and it shows a minimal amount of ads.
Kaz was created in the Republic of Kazakhstan and it focuses in websites written in Kazakh and Russian.
Linkapedia shows the search results from Bing and many other sources like wikipedia using a ranking algorithm called Denis.
Lookseek search engine lets you search the web anonymously, without tracking.
Mail.ru is one of the most popular web portals in Russia and it includes a custom made search engine. It can search text, images, videos and apps.
Mojeek is a British built search engine with more than a billion of web pages in its index and a no tracking policy.
Naver is a very popular web portal in South Korea that uses a custom search engine. It was launched in 1999.
Orange is a French multinational telecommunications corporation which includes a search engine in its web portal.
Parsijoo is a Iranian search engine founded in 2010. Parsijoo is the second most used search engine in Iran.
Qwant was launched in 2013 in France. It complements the results of its own search engine with the search results from Bing. Qwant doesn't track users and it doesn't filter web content.
ScrubTheWeb was launched in 1995 and it includes several SEO tools and tutorials. Scrub The Web respects the privacy of the users and it doesn't share user information.
Seznam was founded in 1996 in Prague (Czech Republic). It's a very popular web portal and search engine in that country.
Sogou was launched in 2004 and it's a subsidiary of Sohu, a Chinese Internet company. It can search text, images, videos and medical information.
Solofield is a new Japanese search engine. It can search text, images and videos.
Sputnik was launched in 2014 in Russia and it's owned by the Rostelecom telecommunications company. It can search text, images, maps, news and medical information.
Superarama is a Turkish search engine that started in 2011. Superarama uses low powered servers in a peer-to-peer network and tries to create a safe search service for young children.
Teoma was launched in 2000 and a year later it was acquired by Ask Jeeves.
WotBox was launched in 2013 and it's committed to protecting the privacy of the users.
Yahoo ! was launched in 1995 and now it's part of the Yahoo web portal which is translated to more than 30 languages.
Yandex is the most used search engine in Russia and it's one of the largest Internet companies in Europe.
Yooz is another search engine from Iran that has more than a billion indexed web pages. It's focused in websites written in Persian.
As a bonus, here you have other popular search engines that might interst you. I couldn't find if they use their own web crawler but they are worth mentioning.
Dogpile was launched in 1995 and it's a metasearch engine that aggregates the results from Google and Yahoo.
Ecosia is the only search engine that plants trees with the ad revenue. Ecosia was launched in 2009.
Enginuity was founded in 2013 by Dan Gardiner and ranks content based on social engagement.
Oscobo was created by two guys from the UK and it respects user's privacy. Oscobo doesn't track the users and it doesn't keep a record of their activities.
Startpage gives you the same Google search results but it respects your privacy. It doesn't track users.
Unbubble is a metasearch engine that aggregates the search results from several other search engines. It ranks the results based on a neutrality assessment.
Webcrawler was launched in 1994 and it's a metasearch engine that uses the results from Google and Yahoo.