Summary: While Google may offer the ultimate search engine and tools, you should not ignore other desktop and Internet search options.
In the world of Web search, there are more than 11 Ways to Search Without Google, although few of them offer compelling alternatives. The main problem with all these general-purpose Web search engines is that they are no better than Google, and a few are probably worse. Take Ms. Dewey for example (figuratively speaking).
I guess, Ms. Dewey can amuse a few male users for a few minutes (until it becomes clear that she ain't gonna get naked), but when it comes to finding information, most of us would rather google.*
Google is likely to remain a Web search leader for a while, but check out AllTheWeb Livesearch (brought to you by Yahoo!). Unlike the maker of the other Live Search (AKA Microsoft), Yahoo! offers a couple of noteworthy innovations:
"Livesearch [...] analyzes your search in real-time and instantly provides Web results with alternate search queries as you type. These suggested queries are based on what other people have searched for. [...] Livesearch makes searching the Web faster and easier by: predicting what you are searching for, suggesting alternate search queries as you type that help you focus your search, and providing relevant results in real-time. It is a big improvement on having to type one search after another to get the results you want."LiveSearch is still in beta, so it has a few quirks. For example, search results for queries that use international characters (such as Cyrillic letters) sometimes display strings of Unicode values (e.g. u0438\u043e\u0433\u0440\u0430) instead of text. I assume these problems will be fixed.
.NET developers out there: try Dan Appleman's SearchDotNet.com. SearchDotNet is based on the Google's custom search engine. Dan claims that it returns more relevant results about .NET programming. (Since I mentioned Dan Appleman, read his Microsoft + Yahoo = Microhoo? article; it's funny.)
Now, what about desktop search? I was never a fan of desktop search utilities built by Microsoft or Google. From my limited experience, they do more harm than good: the original Goggle Desktop Search was a resource hog, while Widows desktop search caused my Windows XP Explorer to crash, so I had to disable its advanced features. If I need to find something on my desktop, I use either the basic Windows Explorer search or the Windows shell find command. Both options are quite limited, so I was really thrilled to find a free Windows Grep tool:
"[Windows Grep] combines the power and flexibility of traditional command line grep utilities available on DOS, UNIX and other platforms with the ease of use of Microsoft Windows. In addition to searching, Windows Grep also performs global replacing in your files, with complete safety. Windows Grep is designed for searching plain-ASCII text files, such as program source, HTML, RTF and batch files, but it can also search binary files such as word processor documents, databases, spreadsheets and executables."While not exactly a search tool, Launchy (freeware) is joining the list of my favorite utilities. After installing and making sure Launchy is running, press ALT+SPACE (you can change this shortcut to something else) and enter a few letters of the name of the application or document you want to launch in the dialog box (e.g. enter "Pain" if you want to start Paint); then just pick the desired item from the list of matches found in the indexed directories (you may need to add your custom folders to the predefined search locations).
In addition to launching applications via a couple of keyboard strokes, you can use Launchy to perform basic calculations. Scott Hanselman suggests a few similar tools, but I haven't tried those, yet.
UPDATE (Nov-29-2007): It looks like Google is catching up with Yahoo!'s LiveSearch. To see the Google's implementation of keyword suggestion, enable the Keyword Suggestion option by clicking the Join this experiment button of the corresponding section on the Google Experimental Search Labs page.
Special Search Engines That Are Not Google or Yahoo
Ten Search Engines You've Never Heard of (And Can't Live Without)
|*||In case you did not know, on June 15, 2006, google became a verb.|