Galoob Babble (1988, LED/Sounds, 4 AA Batteries, Model# 4714)
Interesting little game, apparently you would hit the Record button and record yourself saying something, and then you have a friend hit Play and the machine will play it backwards. Your friend then hits Mimic and trys to pronounce the phrase backwards into the machine to try to figure out what was originally said. There's also a 'Game 2', but I'm not sure what that is. Thanks to Charlie DeTar for pointing out this game to me. He's also written a Java application that emulates this game.
Do I have this? Yes, boxed.