Blogs:

b2evolution

A blog script featuring multiple blogs, categories/sub-categories, skins, search function, multiple languages, search engines friendly URLs
Homepage: http://b2evolution.net/

Nucleus

A powerful blog script featuring multiple blogs, multiple authors, drafts and future posts, bookmarklets.
Homepage: http://nucleuscms.org/

WordPress

WordPress is a personal publishing tool with focus on aesthetics and featuring cross-blog tool, password protected posts, importing, typographical niceties, multiple authors, bookmarklets.
Homepage: http://wordpress.org/

Content Management:

Drupal

An advanced portal with collaborative book, search engines friendly URLs, online help, roles, full content search, site watching, threaded comments, version control, blogging, news aggregator.
Homepage: http://drupal.org  

Geeklog

A portal system with a wide range of modules.
Homepage: http://www.geeklog.net/

PHP-Nuke

One of the most popular community-based portals with a big choice of modules and languages.
Homepage: http://www.phpnuke.org/

Mambo Open Source

A professional level yet easy to use Content Management System featuring inline WYSIWYG content editors, newsfeeds, syndicated news, banners, mailing users, links manager, statistics, content archiving, date based content, 20 languages, modules and components.
Homepage: http://mamboserver.com/

phpWCMS

phpWCMS is perfect for professional, public and private users. It is very easy to learn and gives you the flexibility to separate layout and content. Lots of powerful but simple implemented features assists publishers and web developers too.
Homepage: http://www.phpwcms.de/

phpWebsite

Very powerful Content Management System with document manager, announcements, menu manager, photo album, block maker, FAQ, web pages maker, polls, information categorizer, calendar, link manager, form generator.
Homepage: http://phpwebsite.appstate.edu/

Post-Nuke

A Content Management System with focus on flexibility and security.
Homepage: http://www.postnuke.com

Siteframe

A straightforward content-management system designed for rapid deployment of community-based websites. Nice-looking templates, oriented toward document-sharing, clean interface.
Homepage: http://siteframe.org/

Xoops

A very popular advanced portal system.
Homepage: http://www.xoops.org/

Customer Relationship:

Craftl Syntax Live Help

A Live Help chat system featuring monitor your visitors, proactively open a chat session, multiple chat sessions, referer tracking, page view tracking, multiple operators, canned responses/images/URLs, multiple departments each with different icons, leave a message.
Homepage: http://www.craftysyntax.com/

Help Center Live

Very powerful all-in-one help center including Live Help, Support Tickets and FAQ. Features include unlimited operators/departments, monitor visitors, initiate chat, collect visitor's information, track visitor's footprint, autosave chat transcripts, canned messages, leave a message, auto-assign tickets to operators, unlimited FAQ topics.
Homepage: http://www.helpcenterlive.com/

osTicket

A Support Tickets system featuring email piping, pop3 login, unlimited email addresses, admin/staff/user panels, avoid autoresponder loops, limit maximun tickets user can have opened, accept attachments and limit size, pager alerts for admin.
Homepage: http://www.osticket.com/server/

PHP Support Tickets

A simple, one-admin Support Tickets system featuring self-registering, emailing to admin, attachments.
Homepage: http://www.phpsupporttickets.com/

Support Logic Help Desk

A Support Tickets system featuring multiple email addresses, admin/staff/user panels, canned responses, HTML tags support, email limit on a per user/day basis, attachments.
Homepage: http://www.support-logic.com/index.php

Support Services Manager

Homepage: http://www.sheddnet.net/

Discussion Boards:

PHPBB

A widely-popular open-source bulletin-board package, works well, simple user interface and admin panel, clean look, scales well, and can be customized.
Homepage: http://www.phpbb.com/

SMF

Elegant. Effective. Powerful. Free. SMF is all of the above. SMF is a next-generation community software package and is jam-packed with features, while at the same time having a minimal impact on resources.
Homepage: http://www.simplemachines.org/

E-commerce:

CubeCart

An easy to use yet powerful shopping cart featuring unlimited categories and products, multiple payment gateways, downloadable products. The design is very easy to modify.
Homepage: http://cubecart.com/

osCommerce

A power-user shopping cart with a big variety of modules and support of almost every payment gateway. A big developers community is ready to offer custom solutions depending on your needs.
Homepage: http://oscommerce.com/

Zen Cart

Zen Cart truly is the art of e-commerce; a free, user-friendly, open source shopping cart system. The software is being developed by group of like-minded shop owners, programmers, designers, and consultants that think e-commerce could be and should be done differently.
Homepage: http://www.zen-cart.com/

F.A.Q:

FAQ Master

Unlimited categories/questions/answers, web-based administration.
Homepage: http://www.technetguru.net/design/faqmasterflex.php

Guest Books:

ViPER Guestbook

The ViPER Guestbook is a high end guestbook script that is versatile, reliable, very comfortable and easy to use. The perfect choice for the ambitious webmaster !
Homepage: http://www.vipergb.de.vu/

Image Galleries

4Images Gallery

An Image Gallery system featuring unlimited categories/subcategories, web-based and FTP images upload, auto-thumbnails, comments, send a picture, rate a picture, random pictures, extensive administration panel.
Homepage: http://www.4homepages.de/

Coppermine Gallery

An Image Gallery system featuring categories and albums, thumbnails and intermediate size pics, search feature, new and random pictures, user management (private galleries, groups), user comments, e-cards feature, slideshow viewer.
Homepage: http://coppermine.sourceforge.net/

Mailing Lists

PHPList

A powerful mailing list featuring multiple mailing lists and attachments.
Homepage: http://www.tincan.co.uk/

Polls and Surveys

Advanced Poll

A highly windows-inspired poll script.
Homepage: http://www.proxy2.de/scripts.php

PHPEsp

PhpESP is an effective, capable, web-based survey application that enables businesses to create complex and advanced surveys, view results in real time, and carry out advanced analysis.
Homepage: http://phpesp.sourceforge.net/

PHPSurvayor

Develop, publish and collect responses to surveys. Display surveys as single questions, group by group or all in one page or use a data entry system for administration of paper-based versions of the survey. PHP Surveyor can produce 'branching' surveys (set conditions on whether individual questions will display), can vary the look and feel of your survey through a templating system, and can provide basic statistical analysis of your survey results.
Homepage: http://phpsurveyor.sourceforge.net/  

Project Management

dotProject

Project Management featuring companies, projects, tasks (with Gantt charts), forums, files, calendar, contacts, tickets/helpdesk, language support, user/module permissions, themes.
Homepage: http://www.dotproject.net/

PHPprojekt

Project Management featuring optional group system, privileges, calendar, contacts, time card, projects, chat, forum, request tracker, mail client, files, notes, bookmarks, to-do list, reminder, voting, language support.
Homepage: http://www.phprojekt.com/  

Wiki

TikiWiki

TikiWiki is designed to be an international, clean and extensible Content Management System and Groupware that can be used to create all sorts of web applications, sites, portals, intranets and extranets. TikiWiki also works great as a web-based collaboration tool. TikiWiki has a lot of native options and sections that you can enable/disable as you need them.
Homepage: http://www.tikiwiki.org/

phpWiki

PhpWiki is a web site where anyone can edit the pages through an HTML form. Linking is done automatically on the server side; all pages are stored in a database.
Homepage: http://phpwiki.sourceforge.net/

Other Scripts

Moodle

A Course Management System designed to help educators create quality online courses. Available in currently 34 languages, featuring WYSIWYG HTML Editor, teacher has full control over all settings for a course, flexible array of course activities (Forums, Journals, Quizzes, Resources, Choices, Surveys, Assignments, Chats, Workshops), user logging and tracking, mail integration and much more.
Homepage: http://moodle.org/

Noahs Classifieds

A classifieds system featuring categories and subcategories in unlimited depth, image upload for categories and classifieds, variable fields per categories, customizable email notifications, locking categories, classifieds approval, auto-thumbnail generation, classifieds management by user, send classified to a friend.
Homepage: http://classifieds.phpoutsourcing.com/

Open-Realty

Real Estate listing system featuring attachments, flexible search, template system, Yahoo Maps interface.
Homepage: http://www.open-realty.org/  

PHPadnews

A highly professional complete ad server featuring different types of ads, display based on keywords, zones, hour of the day, day of the week, extensive statistics, client statistics.
Homepage: http://phpadsnew.com/

phpCOIN

A full billing/invoicing application, perfect for webhosting resellers.
Homepage: http://www.phpcoin.com/

phpFormGenerator

A form generator featuring up to 100 form fields, all kind of input fields incl. file upload, customizable fields attributes, send submitted data to an email address or store them in a database, admin panel.
Homepage: http://phpformgen.sourceforge.net/

WebCalendar

A very powerful webcalendar featuring private and public calendars.
Homepage: http://webcalendar.sourceforge.net/