Hand-drawn face portraits (Nigaoe 似顔絵) or charactures are very popular in Japan. You can often find an artists sitting by the side of the road in busy shopping locations or inside shopping malls like you can see in these pictures.
Ishikawa Ryo, the teenage champion Japanese golfer has a picture of himself on his golf ball. At a tournament a few months back, a fan picked the ball up to take home as a souvenir. People in the crowd had to explain to her to put it back on the fairway or she would cause Ishikawa to lose the match.
Another good site to take a look at is one that makes nigaoe for your SNS profile.
Have you had your picture drawn? How was it?