Jaspersoft. Jaspersoft offers a set of open source business intelligence applications ranging from JasperAnalysis for analyzing multi-dimensional data, to JasperReports for creating detailed, and graphical reports on business processes and status. JasperSoft offers both a free Community Edition and a Professional Edition that includes support and services. You can find a breakdown of the differences between these editions here.
Pentaho. The Pentaho BI Suite is also available in a free Community Edition or an Enterprise Edition that includes support and services. You can find webinars on its applications here, and look at what some business are doing with Pentaho here. Pentaho’s suite is modular, and you can either deploy the whole thing, or pick components, such as Pentaho Analysis and Pentaho Reporting.
SpagoBI. SpagoBI is an integration platform for Business Intelligence available in a server version that you can download here. It’s not a distinct set of pre-defined applications, but rather a set of tools that can be modularly customized for unique applications. There is a video on SpagoBI and open source Business Intelligence found here.
Actuate. Actuate’s open source Business Intelligence applications are focused on allowing developers to build Rich Internet Applicaitions (RIA) that can do things like deliver business analytics and data directly to web sites. The company offers a full suite of tools, focused on everything from spreadsheets to reports, and you can find interesting demos here. Actuate founded and leads the BIRT (Business Intelligence and Reporting Tools) open source project within the Eclipse Foundation, and BIRT is at the center of its applications.