For a long time, filesystem lovers have eagerly eyed the indexing and fast search capabilities of database systems, and wished that similar capabilities could be added to filesystems themselves, rather than requiring an intermediate interpretive software layer such as a database application. The best-known and most powerful instance of this sort of filesystem to date is the BeOS File System, BFS. Unfortunately, BFS was tied to the Be Operating System, which was not a commercial success. At one time or another, projects were underway to support connectivity to the BFS under Linux, but these have never materialized in the mainline Linux kernel, and are probably less popular now that the BeOS is officially dead after Be's acquisition by Palm. If the people at Palm are smart, they can get some major PR points by releasing at least the BFS source code as GPL, but who knows? The use and storage capacity of Palm devices are fairly minimal, but I hope that Palm sees what an elegant and powerful filesystem it has in BFS, and at least use it (if not all of the impressive BeOS) in more powerful, future devices that they are hopefully working on.
For Linux, the Reiser4 filesystem is planned to support some level of indexing. Reiser4 is the next generation of the ReiserFS journaling filesystem, and it is actively under development. For more information about ReiserFS, see http://www.namesys.com. It is sometimes hard to figure out exactly what Reiser4 will contain, but indexing has been mentioned often. The site is somewhat unreadable, but there's a lot of information there if you can parse it correctly.