When I was a kid my grandfather always told me that if I swallowed my gum it would take seven years to digest and that it would stick to the inside of my stomach. Being a naïve kid at the time I listened to him and never questioned it even though he was wrong when in reality he was just worried about me choking. Swallowing gum is no more harmful than anything else we consume. The sweeteners get absorbed into the body like vitamins and the rest of the ingredients like the softeners and gum base pass through the body normally.
Swallowing gum can be dangerous though. Doing so on a rare occasion is perfectly fine and healthy but it is not wise to swallow gum frequently. Doing so has on occasion caused intestinal issues such as blockage. You also need to be careful especially with kids because gum does cause a big choking hazard.http://www.medicinenet.com/script/main/art.asp?articlekey=46642