Apache Tomcat is an open source software implementation of the Java Servlet and JavaServer Pages technologies. Apache Tomcat powers numerous large-scale, mission-critical web applications across a diverse range of industries and organizations.
JBoss is Red Hats Java EE 5-compliant (soon Java EE 6-compliant) application server. It is, as with Red Hat itself, dual-licensed either as open source (community edition) or commercially (enterprise edition).
GlassFish v3, built by the GlassFish community, is the first compatible implementation of the Java EE 6 platform specification. Many of the Java EE 6 themes carry over to Sun GlassFish Enterprise Server v3 - flexibility, extensibility, and developer ease of use.
JOnAS is a leading edge Java EE 5 certified Open Source OSGi Enterprise Server by OW2. The License used by JOnAS is the LGPL. The OW2 development community includes many academic institutes (Grenoble University, INRIA, LIFL, Peking University, UPM, ...