There is a few discussions at the Apple support forum on the Apple website. Very strange problem indeed. There was no single solution though and many had no solution.
Theories that were stated included:
1) screen not turning off when talking and your face is pushing buttons
2) Either your voice or the persons voice is a certain pitch that triggers a DTMF tone (the tones when you push numbers on a phone) - it is reported it happens more with higher pitched female voice than male voices.
3) Resetting network settings on the phone fixed it for at least one person
4) Cell phone making beep when switching towers during call
5) Someone is recording your line
Search Google for "keytone during call iPhone"
My phone will chime in when I receive new messages, e-mails and other various notifications. Is the beep that you hear the same sound you use to receive your notifications? Most likely not, but I am hopeful for a simple solution.