If you have no intention of writting an ``++HttpSession++`` object to file, then storing non-``++serializable++`` objects in it may not seem like a big deal. But whether or not you explicitly serialize the session, it may be written to disk anyway, as the server manages its memory use in a process called "passivation". Further, some servers automatically write their active sessions out to file at shutdown & deserialize any such sessions at startup.
The point is, that even though ``++HttpSession++`` does not ``++extend Serializable++``, you must nonetheless assume that it will be serialized, and understand that if you've stored non-serializable objects in the session, errors will result.