These are personalized search engines that let your visitors search just your site... not the whole internet! Very helpful if you have a site with multiple pages, and you want to help your visitors to quickly find what they're looking for.
Even with the best planned out navigation your visitors might not be able to find what they are looking for even if it is on your website. Thats where adding a search box that will search your site (not the entire web) will really add value for your visitors.
The ones below are all free, the first section are remotely hosted, ie. you don't need to install anything or know any coding languages, just cut and paste the provided HTML and you're site is now searchable! The second section is for more advanced webmasters that want a bit more control over their search's result pages and are willing (and able) to install pre-written scripts on their host. Choose whichever works best for you.
Bravenet
The Bravenet Search Engine will spider your website and grab the keywords right off the page! Your search results page is completely customizable so you can make it look just like the rest of your site! They offer tons of other free resources for your website here as well!
Free Find
Want to make your site searchable without a lot of fuss on your end? This one uses the keywords in your pages with "extra weight" on the ones in your meta tags and any others you decide. Hosted on their server, and uses your background and logo on the search pages so it can look like it's on your own site!
Fluid Dynamics Search Engine
Not remotely hosted but I'm listing this as an alternative if the ones above aren't powerfull enough for you. Written in CGI, this is one powerfull search engine! Totally customizable right down to the look of the engine to your own personal algorithm (the formula for deciding what outranks what). Very fast, easy to use (setting it up the first time was a bit difficult, but in all honestly anything that day seemed difficult), and fits seamlessly into a site. I use this here and on a few of my other web sites and love it!