ahCrawler
A PHP search engine for your website and web analytics tool. GNU GPL3
ahCrawler is a set to implement your own search on your website and an analyzer for your web content. It can be used on a shared hosting.
It consists of
* crawler (spider) and indexer
* search for your website(s)
* search statistics
* website analyzer (http header, short titles and keywords, linkchecker, ...)
You need to install it on your own server. So all crawled data stay in your environment.