Liferay is an enterprise portal. It handles users and portlet drawing, has a full administrative interface, supports all the major databases and the main J2EE application servers, and has single sign-on capabilities and multiple language support. It uses Apache Lucene for document searching. A number of portlets are included, including a guestbook, a calendar, a mapping utility which uses Expedia, news, polls, a document library, and live stock information.
Xapian is a search engine library, scalable to collections containing hundreds of millions of documents. It's written in C++ with bindings for Perl, Python, PHP, Java, Tcl, C#, Ruby, and Lua. It is a highly adaptable toolkit that allows developers to easily add advanced indexing and search facilities to their own applications. It supports the Probabilistic Information Retrieval model and also a rich set of boolean query operators. Omega is a Web search application built upon the Xapian library. It can index a Web server's document tree (including HTML, PDF, OpenOffice, MS Word/Excel/Powerpoint/Works, WordPerfect, RTF, PS, etc.), or data exported from arbitrary sources (e.g. SQL databases).
BORG is a calendar and task tracking system written entirely in Java. The calendar is an appointment organizer that provides a nice month view, month printing, email reminders, popup reminders, and a to do list. The task tracker tracks issues and tasks through various user-defined states.