1. Watch a movie. Most commercial airlines offer an in-flight movie. Some will even give you choices.
2. Fire up the laptop/tablet/iPad, etc. and watch movies, listen to music, or play a few games to pass the time.
3. Read a book. Considering most smaller tech devices (like MP3 player.) will not last 13+ hours without a re-charge this becomes a viable option in the last few hours of the flight.
4. Puzzle books. These are popular forms of cheap entertainment and are likely to assist you in your quest for sleep.
5. Chat with the insomniac next to you. If you or the person next to you are the outgoing type, a conversation is a great way to pass the time. You might even make a new friend.
6. SLEEP. I know this list is supposed to be what to do when you are not asleep, but if you can't fall asleep on a boring 13 hour flight, you need to lay off the caffeine and/or sugar.