If you're playing on Lylat Cruise with two of the three characters from the Star Fox series (Fox, Falco, or Wolf), you can have a conversation between characters. Press down repeatedly on the d-pad (so long as your taunts are mapped to the d-pad) during the battle, and the conversation should occur. This can only happen on the Lylat Cruise stage, and only with two of the three characters from the Star Fox series on that stage at one time.

Update: The Star Fox conversations can also occur on the old Melee stage Corneria. (Submitted by modesta106)