I've gotten several questions on this topic so I thought it might be a good thing to show in a blog.  Recording with TAPI 3.1 is actually pretty easy if you are running on Windows XP or better.  TAPI 3.1 provides some simple filename-based methods to dump the conversation into a .WAV file.  If you want to control the file, or stream it somewhere else, it's a bit more difficult and Microsoft provides a decent sample with the platform SDK that does it.

Here's a simple example -- in this scenerio we will create a new outgoing call, connect it and then setup an outgoing stream to play a welcome message:

TapiCall currCall = selectedAddress.CreateCall(numberToDial, LINEADDRESSTYPES.PhoneNumber, TAPIMEDIATYPES.AUDIO);
if (currCall != null)
{
   currCall.Connect(false);
   playbackTerminal = currCall.RequestTerminal(TTerminal.FilePlaybackTerminal, TAPIMEDIATYPES.AUDIO, TERMINAL_DIRECTION.TD_CAPTURE);
   if (playbackTerminal != null)
   {
      playbackTerminal.MediaPlayList = new string[] { MESSAGE_PROMPT };
      currCall.SelectTerminalOnCall(playbackTerminal);
   }
}

When the call is actually connected, then we will start the playbackTerminal stream and begin recording the conversation - this would typically be done in the TE_CALLSTATE handler:

if (e.State == CALL_STATE.CS_CONNECTED && playbackTerminal != null)
{
   // Start the playback message..
   playbackTerminal.Start();
   // Begin recording the conversation - may be half-duplex..
   RecordConversation("RecordedMessage.wav");
}
else if (e.State == CALL_STATE.CS_DISCONNECTED)
{
   // Stop recording when the call terminates.
   if (recordTerminal != null)
      recordTerminal.Stop();

   recordTerminal = null;
   playbackTerminal = null;
}

The code for recording the conversation is pretty simple as well, given a filename, just get a recording terminal and assign it.  TAPI will take care of creating the file and writing contents into it.

private void RecordConversation(string fileName)
{
   // This code only works on XP or better (TAPI 3.1).
   if (currCall != null)
   {
      recordTerminal = currCall.RequestTerminal(TTerminal.FileRecordingTerminal, TAPIMEDIATYPES.MULTITRACK, TERMINAL_DIRECTION.TD_RENDER);
      if (recordTerminal != null)
      {
         recordTerminal.RecordFileName = fileName;
         currCall.SelectTerminalOnCall(recordTerminal);
         recordTerminal.Start();
      }
   }
}

Finis.