"I know who you are."
Translation:Ik weet wie je bent.
If the person to whom you're talking is dressed up, or you're playing a game like "Wie ben ik?", that would be a correct translation.
If you want to tell someone you know them, for example because you saw them on tv, only "ik weet wie jij bent" would be correct.
I have no idea what the game "wie ben ik" is about or why only it allows for that translation.
I figured it is probably better to look up a good explanation in stead of rambling along from my gut feeling: http://www.dutchgrammar.com/forum/viewtopic.php?t=703 seems to offer a good explanation.
To me "ken" feels more directed towards something specific, while "weet" is more general.
I can say " Ik ken je" but not "Ik ken wie je bent" and I cannot say "Ik weet je" but I can say " Ik weet wie je bent".
Because the 'you' in this sentence is a subject as well, so it's 'jij' or 'je'. ;)
I guess you could use zijn with plural version of you (jullie): Ik weet wie jullie zijn. Can anyone confirm/deny?