cancer and Bad Stuff from artificial sweeteners.
There's pretty good evidence that artificial sweeteners don't prevent obesity in the long term, though the underlying cause isn't well known. But there's no solid evidence that they cause cancer:
"In the Nurses’ Health study and the Health Professionals Followup study some excess risk of Hodgkin lymphoma and multiple myeloma was found in men but not in women; no association was found with leukemia. In the NIH-AARP Diet and Health Study, there was no association between aspartame and haematopoietic neoplasms. US case-control studies of brain and haematopoietic neoplasms also showed no association. The NIH-AARP Diet and Health Study and case-control studies from California showed no association with pancreatic cancer, and a case-control study from Denmark found no relation with breast cancer risk. Italian case-control studies conducted in 1991–2008 reported no consistent association for cancers of the upper aerodigestive tract, digestive tract, breast, endometrium, ovary, prostate, and kidney. Low calorie sweeteners were not consistently related to vascular events and preterm deliveries."