In recent years search engines have started charging for 'express submission' services, etc. and some have no moved over to systems where can only submit a site even if you are a non-commercial operation. Listed below are the important sites you can still submit to for free.
Before submitting make sure your site is as complete as you can get it and that you have read through their guides.
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Relevant links:
search engines
Yahoo! - still free to submit if you are a non-commercial site. Yahoo is still considered the number 1 search engine to aim for so I don't think you need much incentive to try to get listed here.
Google - one of the most important search engines out there. It is vital that you submit here and they offer a lot of help for webmasters.
DMOZ: The Open Directory Project - open and free to submit your site to (find the right directory and submit away). This is important as Google (and others) draw their directory listings from here.
FAST/AllTheWeb - another one which also supplies its results to other sites.
Zeal - the non-commercial directory indexing arm of LookSmart which is run by a thriving community of enthusiasts. To submit you have not only got to register as a member but also complete a quiz to test whether you have picked up their style and ethos (although the quiz isn't too difficult - I (Emperor) passed it second time without much reading around as it is largely commonsense). Again LookSmart supply their results to other sites so this is an important one to get listed on.
MSN - commercial sites can get partial listing at LookSmart through MSN (although they are listed below those submissions that paid for inclusion).
AltaVista - one of the oldest search engines and still important as its results feed through into sites like Ask Jeeves (most of the other ways into Ask Jeeves are only pay for sites).
HotBot - another old and important engine. As well as being popular in its own right it is also one of the main sites for attempting to get you site into Inktomi which supplies results to a lot of important search engines.
Alexa - although you will have been indexed if someone has visited the site whilst using the Alexa toolbar you can guarantee a search by adding the URL in here.
NationalDirectory - like a lot of people they take their directory listings from DMOZ but by using the main/central box on this page you can get their robots to index your site.
whatUseek - you have to pay for their main category listings but you can get indexed by their Secondary Index for free 9although they say your results will be ranked lower than those that pay for inclusion).
