Google 
Most popular search engine on the web. Simple, comprehensive, and accurate in producing relevant results. Multiple winner of the Most Outstanding Search Engine by Search Engine Watch readers.

Yahoo!
The web's oldest directory, now also a search engine. If you just want to browse, start here. Great for searching for images, maps, shopping, too.

AskJeeves! 
Search the web by asking it a question in natural language. A neat place to search if you need help putting your topic into words.

AllTheWeb
Owned by Yahoo, this site is a simple web search site, minus the directory experience.

HotBot 
HotBot provides a quick search of its own web listings or that of Google or Ask Jeeves.

Teoma
A smaller index than some of the more popular search sites, but Teoma produces highly relevant results, including link collections by experts and enthusiasts. Also suggests search terms to narrow your search ("refine").