I talk to my alter ego all the time, not only am I a twin, but also I hold conversations with my various alter egos all the time. I usually end up arguing with myself, for no one ever wins. It justs goes around in a circle.
Chess Alter-ego : A True Story??

Yes the ego can be quite annoying. In terms of having discussions with it we all do to some extent. However the truth of the matter is though the illusion of having split personalities and identities exists, we are still a single unity. The inner voice (real you) speaks through different personality facets and ego masks (alter ego, whatever you want to call it) for its own self-amusement as life flies by, but people who meditate and contemplate can usually trace back the original divine source or true voice.

I don't have an alter ego, I just have a huge subconscious personality that's much better at board games than I am. Sometimes when I'm not consciously thinking too hard or if I'm too tired to think at all, I make moves with some sense that they are good moves, without even realizing how good until much later. Sometimes I can set up complicated traps without even noticing until my opponent is just about to fall into them. It's helpful, but it honestly terrifies me sometimes. I'm just afraid of what could happen if I lost all conscious control of myself and my deeper mentality was completely running things. Frankly, I'd rather consciously make stupid mistakes and learn from them, then subconsciously be a genius while learning nothing from it.
Do you know a famous fictional character, Doctor Jeckle? If you do then you would have also known his alter-ego, Mister Hyde.
Many psychologist believe that we all have split personalities. Just recall another fictional character Anakin Skywalker who was taken over by his other personality, Darth Vader -- and what a good example also is The Incredible Hulk.
So far the characters exemplified above shows that either side of their personalities don't get the chance to confront each other in face-to-face scenario. Wouldn't be interesting if they do? I wonder how would Anakin Skywalker and Darth Vader talk to each other. It's crazy as talking to your own self like Golum in the Lord of the Rings isn't it? :-)
What about you? If you were given a chance to see your alter-ego face-to-face and actually can have a conversation to it, how would you handle it?
I explored the idea for myself and got the chance indeed :-)
Wanna know what happened? Read my diary at : http://lacsonplanet.blogspot.com/2008/01/night-i-whacked-my-alter-ego-part-i.html