Gallery is a web based software product that lets you manage your photos on your own website. You must have your own website with PHP support in order to install and use it. With Gallery you can easily create and maintain albums of photos via an intuitive interface. Photo management includes automatic thumbnail creation, image resizing, rotation, ordering, captioning, searching and more. Albums can have read, write and caption permissions per individual authenticated user for an additional level of privacy. Give accounts to your friends and family and let them upload and manage their own photos on your website!
I'd have to add my vote for Gallery. I've used it for awhile now and am very impressed with the results. When you go to their website, check out some of the sample galleries to get a feel for what's possible.