Never use the anti-patterns entitymanager-per-user-session or entitymanager-per-application (of course, there are rare exceptions to this rule, entitymanager-per-application might be acceptable in a desktop application, with manual flushing of the persistence context). Note that some of the following issues might also appear with the recommended patterns, make sure you understand the implications before making a design decision:
1. An entity manager is not thread-safe. Things which are supposed to work concurrently, like HTTP requests, session beans, or Swing workers, will cause race conditions if an EntityManager instance would be shared. If you keep your Hibernate EntityManager in your HttpSession (discussed later), you should consider synchronizing access to your Http session. Otherwise, a user that clicks reload fast enough may use the same EntityManager in two concurrently running threads. You will very likely have provisions for this case already in place, for other non-threadsafe but session-scoped objects.
2. An exception thrown by the Entity Manager means you have to rollback your database transaction and close the EntityManager immediately (discussed later in more detail). If your EntityManager is bound to the application, you have to stop the application. Rolling back the database transaction doesn't put your business objects back into the state they were at the start of the transaction. This means the database state and the business objects do get out of sync. Usually this is not a problem, because exceptions are not recoverable and you have to start over your unit of work after rollback anyway.
3. The persistence context caches every object that is in managed state (watched and checked for dirty state by Hibernate). This means it grows endlessly until you get an OutOfMemoryException, if you keep it open for a long time or simply load too much data. One solution for this is some kind batch processing with regular flushing of the persistence context, but you should consider using a database stored procedure if you need mass data operations. Keeping a persistence context open for the duration of a user session also means a high probability of stale data, which you have to know about and control appropriately.