Here are the conclusions of some research studies looking at artificial sweeteners and cancer:
Conclusion: The results of this carcinogenicity bioassay confirm and reinforce the first experimental demonstration of [aspartame]‘s multipotential carcinogenicity at a dose level close to the acceptable daily intake for humans. Furthermore, the study demonstrates that when life-span exposure to [aspartame] begins during fetal life, its carcinogenic effects are increased.
Conclusion: Despite some rather unscientific assumptions, there is no evidence that aspartame is carcinogenic. Case–control studies showed an elevated relative risk of 1.3 for heavy artificial sweetener use (no specific substances specified) of >1.7 g/day. For new generation sweeteners, it is too early to establish any epidemiological evidence about possible carcinogenic risks. As many artificial sweeteners are combined in today’s products, the carcinogenic risk of a single substance is difficult to assess. However, according to the current literature, the possible risk of artificial sweeteners to induce cancer seems to be negligible.
Conclusions: Our findings do not support the hypothesis that aspartame increases hematopoietic or brain cancer risk.
Conclusion: The present work indicates a lack of association between saccharin, aspartame and other sweeteners and the risk of several common neoplasms.
So it looks like there’s some controversy but the majority of the research indicates that Diet Coke is in the clear.