How many search engines are there on the web?

There is no possible way to tell that, several search engines use many sub search engines in whats called cluster service. not to mention that search engines do not have to register themselves with any entity, if you wanted to you could setup a proxy server service to do a search engine function in your own home for the cost of the computer to run it around 500 bucks and about another 200 for the software and additional hardware required. So to answer the question it's beyond millions but if your looking for search engines based around a business all the ones i can think of are

ask.com
dogpile.com
google.com
yahoo.com
msn.com
then any other website that has a "search the web function" thats a search engine so thats why it's not possible to tell.