Can swallowing too much chewing gum really cause an obstruction in the appendix?

No: The only real risk, and its rare, is something called a bezoar (indigestible material) which can cause an obstruction in the digestive tract. However, the risk is very rare, and your appendix is not generally at risk. If you imagine the number of people, especially kids, who swallow gum all around the world every day, the risk of choking on a piece of gum is much higher than anything else.

A/W Dr. Perkins: Usually there isn't a problem as the gum will pass harmlessly through the body. However, there are rare cases of chewing gum bezoars which have occurred causing esophageal ; intestinal obstruction (http://pediatrics.Aappublications.Org/content/102/2/e22.Full).