BuddyPress - WordPress social networking in a box.

EssentialPIM - EssentialPIM is a free Personal Information Manager that keeps up with the times and lets you manage appointments, tasks, notes, contacts, password entries and email messages across multiple devices and cloud applications.

Elgg - Opensource social network engine

Todo.txt - Track your tasks and projects in a plain text file, todo.txt. A todo.

HumHub - HumHub is a free social network software and framework built to give you the tools to make teamwork easy and successful.

Task Coach - Task Coach is a simple open source todo manager to keep track of personal tasks and todo lists.