

The most important place to submit your web site is not to search engines, but rather to search engine directories. Smaller and even large search engines regularly add content based on the directories. If you have a local site, make sure you submit to Yahoo local directories and online yellow page sites.
Google has a search engine submission button here. However, it is recommended that you submit a sitemap via Google Sitemaps (Beta). Sitemaps offers statistics and analysis. An easy way to create a Sitemap is to go to xml-sitemaps and follow the instructions. NOTE: You can also add your sitemap to Yahoo from the home page.
Yahoo has two submission areas (see the note above), their search engine and their directory. If your web site is for profit, you will have to pay to get into the Yahoo Directory. Although somewhat long-winded, SelfPromotion offers a comprehensive explanation of getting into the Yahoo directory, plus all the links.
I don’t have much success here but you should try this. If an editor happens to be in your category you will probably get into DMOZ within several weeks. You MUST follow their instructions carefully. Here is the DMOZ link.
There are specific directories in many fields – science, health and so on. Do a search on “health” directories or whatever your category is and then submit to the appropriate search engines.
Search Directories usually do not have spiders so you must submit by hand. Since people (editors) are checking your submission, make their life easier by keeping to the rules. Before you begin, create a text file with the following information:
If your home page is linked from relevant, high-ranking sites, the chances are it will be indexed in the major search engines after a few months. Search the major search engines (I list some below) for your home page (ie. http://www.mysite.com/index.html). If it is listed, you don’t have to do anything else.
If your home page is not listed, submit it manually on the major search engines. Your page will not be as well ranked if you submit it to the search engines. Your page receives a better ranking if it is picked up automatically by the search engine spiders or bots.
Do not resubmit your home page more than every 45 days or so or you may be seen as a sp@mmer. Take notes when you submit and where.
AddMe, Aeiwi, Aesop (includes ExactSeek), Alexa Crawl (Alexa uses DMOZ listings), BigFinder, BlogCatalog, Cipinet, Entire Web, INeedHits, InfoSpace, Jayde, MSN, ScrubTheWeb, SearchIt, WhatUSeek