[Feel free to add your own recommendations using the same format]
Gallery 2http://gallery.menalto.com/This is a powerful and flexible image gallery. There are a number of templates provided but eventually you will probably want to customize or create your own. It seems to me better suited to a personal gallery than a community gallery.
Copperminehttp://coppermine-gallery.net/Another popular image gallery, this one (IMO) better suited for a community.
SMFhttp://www.simplemachines.org/A full-featured forum. Good performance. My only gripe is that there's no really good blog integration. Has a quite complex permission system, so some care is needed in managing that side of things.
PunBBhttp://punbb.org/A simpler and easier-to-manage forum than SMF. I'm not currently using it but I'd use it again for a smaller site.
CMSMadeSimplehttp://cmsmadesimple.org/Robust and flexible content management system. Essentially a web-based interface to allow you to create and edit sites. Works well for sites that you would otherwise use an offline tool for, but with a lot more flexibility. You need to know CSS to get very far with customizing the look and feel. Nice interface for managing plugin modules. Not so great for giving to clients for editing.
Wordpresshttp://wordpress.org/"The" blog. Very very simple to set up and use. Customizing takes more work. I think this would be a great starting point for anyone interested in learning how to set up dynamic websites. You'll have to watch the comments though, blogs are spam magnets...
MediaWikihttp://www.mediawiki.org/The ultimate wiki code. Great for building "knowledge" sites and for collaboration on same. The syntax puts some people off, but you get used to it. Easy install, customization is tricky because, like the front end, the back end works differently than most other web software.
There are a lot of scripts that can be run as demos here:
http://www.opensourcecms.com/
