How do I share sessions across web apps?
You cannot share sessions directly across web apps, as that would be a violation of the Servlet Specification. There are workarounds, including using a singleton class loaded from the common classloader repository to hold shared information, or putting some of this shared information in a database or another data store. Some of these approaches have been discussed on the [WWW] tomcat-user mailing list, whose archives you should search for more information.
Sharing sessions across containers for clustering or replication purposes is a different matter altogether.
Other containers may provide a non-spec way of doing this.