PHP5 supports SQLLite (
http://www.sqlite.org/) which is a stand-alone binary flat file that can just sit in the www document root and is structured as a database. It's pretty powerful if you don't have a SQL server available to you and from what I've seen SQLLite works pretty well but it is a memory hog.
There is also writing PHP in such a way to support flat text files. I would highly recommend against this route. It would open up security holes in your server and the possibility of file corruption (i.e. a field that is in the wrong location in the text file) is high. Parsing text is also a fair amount of overhead.