Some of these are search indexes (Alta Vista, Google, Infoseek, Lycos), others are subject directories (Yahoo!, LookSmart, WebCrawler). There are over 500 search engines of one kind or another; while these are some of the best, this is certainly not a comprehensive list. Many of them, including MSN Search, HotBot, AOL Search, and Overture, are powered by Inktomi's search engine, so their search responses will tend to be similar. 

You should be aware that many for-profit search sites accept paid listings that automatically get placed on top of other sites. Additionally, many portal sites, such as AOL, Yahoo!, MSN, and others, place affiliated or owned sites above other listings. Some engines will only list sites that have paid for inclusion, and naturally, these are the least useful and comprehensive ones. There are plenty of search sites out there that aren't listed, but some of them are commercially-driven or tied into other sites. Worse, some putative search sites actually "hijack" your browser into receiving a barrage of pop-ups and ad-based displays.

100 Hot Sites (directory listing currently hot sites in various categories)
www.100hot.com/index.html

About.com (formerly Mining Co.; human guides here have compiled lists of what they consider to be the best sites, organized by subject; the Mining Co. addresses still seem to work, at least they did when I last checked)
www.about.com/ OR home.miningco.com/

Ah-ha (pay-to-list search engine that uses AI technology to increase relevance of links displayed)
www.ah-ha.com/

AllTheWeb (formerly FAST Search; Lycos-affiliated search engine whose goal is to index the entire Web every few weeks; right now they're at 300 million; highly rated in a recent comparison study; now indexing MS Word documents stored online)
www.alltheweb.com/

Allwhois (compendium of various countries' "whois" domain lists)
www.allwhois.com/

AltaVista (one of the best power searchers around; use the phrase host:domain keyword, as in host:cnn.com clinton, to search a specific site; the phrase host:country keyword, as in host:uk football, will take you to that country's keyword-associated sites; recently expanded to make searches for multimedia content easier; new "family filter" restricts searches to non-objectionable sites, mostly. Make use of the Sort By feature for best results)
www.av.com/ or
www.altavista.com/

AltaVista Zip2 (a site that specializes in business listings)
www.zip2.com/

Anonymous FTP FAQ List (covers ins and outs of FTP sites, including many, many links -- unfortunately, the list is somewhat old and a goodly number of the links are dead)
hoohoo.ncsa.uiuc.edu/ftp/faq.html

Anzwers (an Australian/New Zealand site)
www.anzwers.com.au/

AOLSearch (formerly AOL NetFind -- NetFind used Excite's search engine, but AOLSearch is based on Inktomi's search engine; pushes you towards AOL content and AOL affiliates)
www.aol.com/

Ask (formerly Ask Jeeves)
www.ask.com/

Atlas Greek Search (largely displays in Greek)
search.hol.gr/

Atomica (small, free downloadable utility that helps you hunt up online word definitions, encyclopedia entries, stock prices, news clips, book references, and Web links; formerly GuruNet)
www.atomica.com/

Beaucoup (combination directory and metasearch site, with connections to 2500+ search engines, directories, and indices)
www.beaucoup.com/

Bigfoot (click on the Web Search tab; uses the Overture/Inktomi engine)
www.bigfoot.com/

Britannica Internet Guide (searches the Web along with its proprietory database)
www.britannica.com/

Canada.com (search engine specializing in Canadian content)
www.canada.com/home/

Citysearch (not a search engine per se, but an online database of information about numerous American metropolitan areas)
www.citysearch.com/

CompletePlanet (claims to be able to access the 100,000+ "hidden" Web sites out there that conventional search engines can't catalog; uses LexiBot technology)
www.completeplanet.com/

DirectHit (subsidiary of "Ask Jeeves" that analyzes the search results of millions of other Internet users to determine the most relevant sites for your search request)
www.directhit.com/

Ecola Newsstand (a virtual newsstand that offers unlimited access to the publications it mirrors)
www.ecola.com/

Electric Library Personal Edition (online library that accesses newspapers, magazines, books, TV and radio transcripts, photos, maps, etc. -- it's free for 30 days, then either $10 a month or $60 a year. Searches only its own content, not the entire Web, but its content is enormous)
www.elibrary.com/

Euroseek
www.euroseek.com/

Exact One (digs through the databases behind the Web sites to find services, job postings, photos, consumer goods, or people)
www.exactone.com/

Excite (general searches often turn up rafts of irrelevant sites; use the "Select words to add to your search" function to narrow things down; also see the streamlined "Excite Precision Search;" be prepared to sort through more adult-oriented sites than the average search engine results provides)
www.excite.com/

FedWorld (search engine for the US Government's web sites)
www.fedworld.gov/

FindWhat (pay directory that gives high bidders prime positioning in the engine's search listings; not an appealing way to run a search engine, but here's the link anyway)
www.findwhat.com/

Galaxy (claims to be the first Internet search directory; filters sites for sexual, hate, and heavily violent content)
www.galaxy.com/

Google (probably the best standalone search engine out there; also has an undocumented mapping capability enabling users to simply type in a street address and be given street maps, as well as offering a toolbar for MSIE; currently offers over 3 billion listings; doesn't bother with Boolean search phrases, but is very sensitive to the use of quotation marks around phrases; try the Google Directory)
www.google.com/

Google Labs (keep an eye on what's cooking at Google)
labs.google.com/

Google Watch (anti-Google site that purports to prove Google threatens our surfing privacy)
www.google-watch.org/

HotBot (now a metasearch engine featuring Fast, Google, Inktomi, and Teoma)
www.hotbot.com/

HotLinks (a directory with a different approach; only links added by members appear in the listings, and the rankings depend on how many visits are made by members)
guide.hotlinks.com/

ILor (engine built on top of Google, providing several options Google doesn't; try the LorLinks feature, which appears when you let your cursor hover over a link on the results page)
www.ilor.com/

Infoseek (now part of Disney's Go! internet service; it likes the pipe character | to narrow down its searches, as in cartoons|flintstone; with Disney's reorganization of the Go service, Infoseek is currently in question)
infoseek.go.com/

InfoSpace (the powering site behind lots of online directories)
www.infospace.com/

Invisible Web (purports to be the "search engine of search engines;" designed to help surfers find hard-to-locate material)
www.invisibleweb.com/

Kenjin (downloadable, highly configurable search utility that uses a proprietory search engine to suggest Web sites related to a particular topic)
www.kenjin.com/

Link Popularity (search engine that hunts down the search engines that are linked to yours -- currently it only works with Google, AltaVista, and HotBot -- and through those links, find out who is linking to your site)
www.linkpopularity.com/

Linkmaster
linkmaster.com/

LookSmart (a directory similar to Yahoo!, but badly organized and featuring much less content; LookSmart Live is a community of users providing search info; recently switched to a pay-for-placement model)
www.looksmart.com/
 

LookSmart has several country-specific sites also, currently including Australia, Canada, Hong Kong, Malaysia, the Netherlands, New Zealand, Singapore, and the UK. All are linked to LookSmart's home page.

Lycos (comes with an optional filter called SearchGuard that screens out questionable content; directory content comes from Fast Search)
www.lycos.com/

Monkey Sweat
www.MonkeySweat.com/

MSN Web Search (combines LookSmart and Inktomi engines; often produces a swarm of adult-oriented links)
search.msn.com/

My Search Engines (site that lets you configure your own multiple search page; useful for specifying specific engines for specific search types)
www.mysearchengines.com/

NBCi Search (formerly Snap!)
www.nbci.com/

Northern Light (strong power searcher, one of the most respected search engines on the Web and a favorite of researchers; offers a fee-based database service in addition to its free search capabilities; organizes search results into easily used folders)
www.northernlight.com/

Oingo (a DMOZ-based directory similar to About, AOLSearch or Yahoo!)
www.oingo.com/

OneLook Dictionaries (search engine for a variety of online dictionaries)
www.onelook.com/

Open Directory Project (strives to be the largest human-maintained directory on the Net)
dmoz.org/

Overture (formerly GoTo)
www.overture.com/

Pandia Search Central (a directory of search engines)
www.pandia.com/

PCBeacon (search engine slanted towards business users)
www.pcbeacon.com/

PeaKaBoo (family-friendly, open-directory search site)
www.PeaKaBoo.Net/

PepeSearch (portal/search site powered by FAST Search, and targeting college/university student audiences more than most others)
www.pepesearch.com/

PhiBot (search engine restricted to math and science topics)
phibot.org/

Raging Search (AltaVista-powered engine that promises to make your searching simple yet effective)
www.raging.com/

Search (a C|Net-affiliated directory powered by Infoseek)
www.search.com/

Search King (recently revamped)
www.searchking.com/

Searchgate Web Directory (focused on teen and young adult surfers)
www.searchgate.co.uk/

Slider (relatively new Web directory with over 2.5 million entries, a free encyclopedia, FTP search, and more)
www.slider.com/

Starting Point (a directory similar to Magellan or Yahoo!)
www.stpt.com/

SureSeeker -- AVOID THIS SITE. It is not a legitimate search engine, but the home of a virus which hijacks browsers and forces them to revisit the site again and again. See my MSIE page for the method to purge this virus from your system. Other sites involved in this scam are www.JetHomePage.com/ and www.searchengine2000.com/ ; avoid them all.
www.sureseeker.com/ (no link provided)

Teoma (new "smart" search engine on the block from the people who brought us Ask Jeeves; try the search term enhancements)
www.teoma.com/

Vivisimo (new search engine that organizes searches into "folders" much like NorthernLights; combines results from AltaVista, Lycos, Yahoo, and DMOZ; unfortunately, it opens pages within its own frames)
www.vivisimo.com/

Web Search
www.web-search.com/

WebBrain (puts a graphical interface on the DMOZ Open Directory listings)
www.webbrain.com/

WebCrawler (a directory powered by Excite)
www.webcrawler.com/

Webhelp (provides actual people to assist in your search using chat clients; quite time-consuming)
www.webhelp.com/home/

WhatUSeek (provides intranet search engines for individual Web sites along with a Web search engine and personal portals)
www.whatuseek.com/

Whois (find out who's behind a particular Web site)
www.internic.com/whois.html

Wisenut (configurable combination directory and search engine; displays sites within its own frame)
www.wisenut.com/

Yahoo! (still the best general Web directory available; put their directory catalog to use to narrow down your searches; does not use Boolean terms like AND or OR, but does use + or - to indicate words that must or must not be in the search results; now uses Google for its search engine)
www.yahoo.com/

Yahoo! Search (more generalized search engine that includes an extended search box for more refined searches, and a tabbed menu for specifying whether a search should sift general Web information or look through news, yellow pages, or images)
search.yahoo.com/

Yep (Web directory/portal that attempts to sort sites by user popularity; gives users the chance to add their input; currently only lists HotBox Web tracking subscribers' sites)
www.yep.com/