eXist-db is an open source database management system entirely built on XML technology. It stores XML data according to the XML data model and features efficient, index-based XQuery processing.
This project started from my frustration that I could not find any simple, portable XML Parser to use inside my tools (see CONDOR for example). Let's look at the well-known Xerces C++ library: the complete Xerces project is 53 MB! (11 MB compressed in a zipfile). I am currently developping many small tools. I am using XML as standard for all my input /ouput configuration and data files. The source code of my small tools is usually around 600KB.
Sphinx is a full-text search engine, distributed under GPL version 2. Commercial license is also available for embedded use.
Generally, it's a standalone search engine, meant to provide fast, size-efficient and relevant fulltext search functions to other applications. Sphinx was specially designed to integrate well with SQL databases and scripting languages. Currently built-in data sources support fetching data either via direct connection to MySQL or PostgreSQL, or using XML pipe mechanism (a pipe to indexer in special XML-based format which Sphinx recognizes).
As for the name, Sphinx is an acronym which is officially decoded as SQL Phrase Index. Yes, I know about CMU's Sphinx project.