Commercial OS X Server, also Open source/cross-platform
Implementation of CardDAV. Available as part of the OS X Server software. Also open source. Python-based.
Open Source
Baïkal is an open-source, lightweight PHP+SQLite CALDAV+CARDDAV server based on SabreDAV.
Open source/cross-platform - in progress
Implementation of CardDAV. Java-based.
Open Source/PHP/PostgreSQL
Implementation of CalDAV Access and Scheduling with web-based administration and CardDAV support.
Free
EGroupware is an enterprise ready groupware server that is adding CardDAV support.
Shareware/Trial Period
CalDAV and CardDAV support.
Unified messaging server
Implementation of CardDAV. Available as part of the Kerio Connect server software.
Open source / Cross platform
Meishi is a Rails 3 based standalone CardDAV server.  It's designed to be lightweight and simple to configure.  Meishi provides both a CardDAV and a simple browser based interface.
Open Source
ownCloud is an open source, simple cloud server, providing WebDAV, CalDAV, CardDAV, etc. It's written in PHP and can use SQLite or MySQL databases. So it runs under Windows, Linux, etc.
Open source / Cross platform
Radcale is an open source cross-platform CalDAV and CardDAV server written in Python. It requires few software dependencies and is pre-configured to work out-of-the-box.
Open Source
SabreDAV is a free WebDAV server and includes support for CardDAV.
Open Source
ScalableOGo (SOGo) is a free groupware server and includes support for CardDAV.
Apache
Apache-based CardDAV server implementation.