I've seen websites offering, for a fee, to submit your website to hundreds of thousands of search engines. Are there really that many?
It's unknown exactly how many search engine websites there are on the web. Certainly thousands, if you include what are really hobby sites.
95% of all search engine traffic is generated by a very small number of search engines. In the region of 100. However, the majority of that traffic actually depends on only a few truly unique databases, operated by Google, Yahoo, and Microsoft.
For example, the Google index is used for the search results delivered on Google (of course), but also on AOL, and ASK (previously known as Ask Jeeves).
The remaining 5% of traffic coming from largely unknown search engines still accounts for a significant amount of users and daily searches, collectively. Individually, however, they should not form part of your marketing strategy.