As a precaution, I will delay circumcising a baby who has a bilirubin count above 16, unless the numbers are going down. Other mohels will run away from a baby with the number 12 or higher. [I have actually been called to do a bris on several occasions because the pediatrician said it was OK and the parents wanted to have the bris at the proper time, but the mohel they initially hired was scared to do it because he felt the bilirubin count was too high. All brisses went well and babies were fine afterwards.]
The one time I delayed a bris to a different day on account of jaundice (at least the one I recall most vividly, though there were probably others) was when the child's bilirubin count was 22 - he looked like a banana from across the room - and the bris was supposed to be on Shabbos. Since it wasn't feasible to check the baby the night before or the morning of (on account of Shabbos), we pushed it off, and the baby ended up being ready by Sunday.
I recently found this article that explains Jaundice in a very clear manner. It was written by Rabbi Josh Flug, a colleague (and client!), and is worth reading from beginning to end.