Introduction
Gallery is a web based organizer of photos that runs on PHP and MySQL. Gallery is also highly customizable as it supports themes and modules for easily extending default functionality. This is open source software that is freely available for download.
Getting Started
LifeHacker has an article on how to install and get started with Gallery. My only comment is that you confirm that your php.ini file has the memory_limit option set to 16MB or higher before installation to avoid out of memory conflicts with the PHP scripts during installation.