Favorite search engines are a matter of taste, and most people these days like the favor of Google. So do I. I tend to use Google first and look elsewhere later. In most cases, Google gets me what I need. [Tip: Google search commands are explained on the More Search Help page. See also Google Search Features. To see your search history and/or to delete it, go to Google History.]
For follow-up work I tend to use Bing or meta-search engines -- the ones that search many other search engines at once, such as ixquick, Dogpile and Metacrawler.
Following are some specialty search engines that target certain types of content. Quality varies greatly, but sometimes these can be helpful.
Blogs: Try Clusty, Ask.com, Waypath, Technorati and/or Icerocket. The Justia Blawg Search and the Law Blog Directory search law-related blogs. The Cornell Law Library's Legal Research Engine searches academic law blogs.
Lexis offers a fee-based general blog search (NEWS;BLOGS) or you can search blogs in various subject areas in the list of individual news publications (News & Business > Individual Publications).
Books: Google Books and Hathitrust are both designed to search the full text of large book collections. See also "Books" and "Book Stores."
Discussion Groups: Try
Yahoo! Message Boards, BoardTracker and/or Omgili.
Facebook: Open Status Search searches recent public Facebook posts. See also "Social Media and Social Networks," below.
Government (U.S.): Try USA.gov. If you know you are looking for a ".mil," ".gov" or ".edu" site, you can try www.SearchMil.com, www.SearchGov.com or www.SearchEdu.com, each of which use Google technology.
Legal: The Legal Research Engine, LawRunner, Quest and LawCrawler are supposed to limit their results to legal and law-related Web sites. I have not had much success with any of them. Google Scholar searches for cases and articles if you click the "Legal opinions and journals" radio button.
Listservs: See "Discussion Groups," above.
Medical: Try www.healthline.com.
Podcasts: Podcasts are digital audio files created in MP3 format. They can be downloaded, stored, saved and listed to at your convenience, but they aren't necessarily easy to find. For a specialized podcast search engine try doubletwist Podcasts. If you download the free software, you can also find podcasts in the iTunes Store.
RSS Feeds: Try Feedster.
Science: Try scienceresearch.com.
Social Media and Social Networks: Try Spock, Wink, Pipl, PeekYou, and/or the more business-oriented ZoomInfo. Hshtags searches hashtags (e.g., #epicfail) across several social networks.
Twitter has its own Advanced Search, or you can try Try Topsy for another perspective. You can search deleted tweets by the U.S. president, congress and governors using Politwoops.
See also "Facebook," above.
Videos: Video search engines include BlinkX, Bing,
For more information about search engines, visit Search Engine Watch. Wikipedia posts an extensive List of Search Engines.