Does GlassFish support active and passive clusters?

Yes and no. In GlassFish, cluster instances talk to each other for health monitoring through GMS (of Shoal). The buddy instances talk to each other for replication of the session state. When a failure is detected, the load balancer can failover the request to any instance in the cluster. The session in question will be fetched from a replica to this instance to continue the conversational state of the session. In this sense, we have an active cluster.

GlassFish does not have a concept of a standby or passive cluster that will take over when an active cluster fails altogether.
That is usually considered a high-cost approach for redundancy and not advisable.

This thread contains more discussion about this topic.

NOTE: This question along with many others was originally answered in the following blog posts from Arun, which might also be of interest:

http://blogs.oracle.com/arungupta/entry/glassfish_delhi_university
http://blogs.oracle.com/arungupta/entry/glassfish_bangalore_chennai_and_pune

All of Arun's Q & A blog entries are available here.