I get asked about this all the time and finally came across ZoomSearch a few weeks ago. After trying it out, I've decided to include it in a new site I'm working on. The free solution is perfect for little sites that don't have big budgets but still want a simple search feature.
ZoomSearch is easy to set up and free for small sites up to 50 pages. The "Standard" version will index 100 pages for $49 US, the "Professional" solution is only $99 US and will search up to 100,000 pages. The unlimited "Enterprise" license is only $299 US.
You run their software from your desktop and specify file types and locations. The tool indexes your site and compiles a few files. You then upload the files to your server and you're good to go.
The search box, extended search and results pages are simple to integrate with your site too.
WrenSoft Website Search Engine Software
Enjoy.