Can it happen that a phone conversation between two people occurs, and at the end one party says to the other that their call has been taped and will be kept on file?  I thought you had to be told that the conversation was being recorded and give permission.

This area is governed by state law.  In some states (for example: New York) it is perfectly legal to secretly tape a conversation with another party.  As long as one party (the taper) is aware of the taping, there is no legal impediment.

Other states differ.  A well known example which highlights this varience is the case of Linda Tripp and Maryland state law.  In Maryland one cannot secretly tape a conversation in which you are a conversant; it is considered to be eavesdropping.  Same thing in New Jersey and some other states.

Of course, taping a conversation to which you are not a party is illegal in all states-- it is eavesdroping.

In CA it is a crime (misdemeanor I think) to tape a phone call unless the person being taped is told.  A recent CA appellate case held that the CA law was not violated, however, when a CA woman's discussions with her stock broker (whose office was in Atlanta, GA) were recorded by the broker

not legal advice...
just a website on the issue
http://www.citizensinvestigations.com/audio/reclaws.html

it is legal if one of the parties is aware of the taping.

TRUE! Here in Tennessee,as long as "1" person knows the conversation is being taped(that would be the person taping),it IS legal.Check the state laws of whatever state you are in,as each state is different w/ ea. law