Everyone knows the story of why Khan knows Checkov...
When Khan was invited aboard the Enterprise, he was also invited to dine with the Captain in his mess. Now this was a very fancy occasion, with the opportunity for Kirk to impress his guest with some very exotic cuisine, indeed. Well, Khan, having been in stasis for.. what... two centuries.. well his stomach was not quite up to this new "blast from the future" that Kirk had bestowed upon him. Excusing himself from his host, Khan hurried down the corridor toward the nearest latrine. Upon entering the latrine he desperately attemped to enter the one stall that was present. Unfortunately, that stall was then occupied by one Ensign Pavel Checkov, who had some business of his own to attend to. Despite the cajoling, banging (actually causing damage to the titanium stall door), and general pandemonium that ensued, Kahn was unable to convince the young Ensign to hurry things up, resulting in , well , kind of a messy experience. As Checkov finished up and departed the stall, Kahn looked at him and said:
"YOU! YOURS IS A FACE THAT I SHALL NEVER FORGET!!"
..anyway, now you know the story.