I remember reading back in the early 90s a number of studies that showed elevated risks of certain brain cancers from aspartame. The evidence was pretty strong - it wasn't conclusive (hence the "possibly" qualifier in this label), but it was enough that I was personally convinced. The link between aspartame and cancer is much stronger than the one between cyclamate (banned in 1970 but legal in the EU) and cancer. My parents never let me chug Sweet'n'Low packets the same way I chugged sugar packets because of it.
IIRC, the only reason aspartame was not banned was because saccharine had just been, and if you banned aspartame there would have been literally no artificial sweeteners on the market. That is no longer the case, with sucralose (Splenda), acesulfame potassium (Coke Zero and other diet sodas), Stevia, sorbitol, and several other sweeteners now on the market.
IIRC, the only reason aspartame was not banned was because saccharine had just been, and if you banned aspartame there would have been literally no artificial sweeteners on the market. That is no longer the case, with sucralose (Splenda), acesulfame potassium (Coke Zero and other diet sodas), Stevia, sorbitol, and several other sweeteners now on the market.