My goal with this thread is to catalog alternatives to cloud services, that can be hosted on one's own server. The goal in all of these cases is to maintain the convenience of cloud services (the ability to access the cloud service no matter where you are), while gaining the privacy benefits of self-hosting those cloud services.
This list is gonna be pretty bare at first, mind you. I'll group things by cloud services, and then what packages replace them.
If you've got a suggestion for a cloud service replacement, post it up. If there's a cloud service that you use, and you want suggestions for a replacement, post away.
Google+
Diaspora* - requires Ruby and either MySQL or PostgreSQL, and prefers nginx (but Apache should work as well) - may have performance issues
Google Reader
Tiny Tiny RSS - requires PHP and MySQL, has an Android client app