AltaVista - Good ol' AltaVista. I remember it from back before the advertisements. I really like its advanced search capabilities, particularly being able to search for an image: or within a domain. It's also nice with Ask Jeeves integrated.
Ask Jeeves - Kind of a mixture of a search engine and a reference librarian. Type a simple question in English and get some good answers.
Google - My favorite search engine. Returns excellent results when trying to find general information sites. So good that I'm often feeling lucky. Don't wade through pages of useless results anymore.
Google Instant Search - This is a bookmarklet that I use all the time to search Google. To use, create a bookmark with it, then simply select some text and click the bookmark. If no text is selected you can type some words to search for.
Mining Co, The - Perhaps not strictly a search engine, but often gives me the information I want. Human "guides" search the web for the best sites on a topic and create a list of links. It again proves that "HUMANS do it better!" as DMoz has said all along.
NewHoo, the Open Directory Project - Yep, I use this all the time, as well as editing it. Great results and almost no broken links! It just keeps getting better and better.
Suite101.com - Perhaps not strictly a search engine, but a nice complement to the Open Directory Project, none the less. A nice mix of rated links as well as original editorial articles and reviews.