One of the world's most common artificial sweeteners is set to be declared a possible carcinogen next month by a leading global health body, according to two sources with knowledge of the process, pitting it against the food industry and regulators.
It looks like the actual research suggests that you can have the amount of aspartame in 12-36 cans of diet soda before you increase your cancer risk, so even if you stay on the conservative side of that, and say "no more than 12 cans," I think most people don't have to change their aspartame intake in response to this. You should definitely talk to your doctor about it if you already have a high cancer risk, or really like diet soda, or just want more reliable information than you can get online.
I think the more useful takeaway from this article is that beverage companies are trying to keep aspartame from being declared a possible carcinogen. That's hardly surprising, but it seems more verifiably true than the proposition that aspartame is a significant carcinogen. A lot of things can increase cancer risk slightly, but much fewer increase cancer risk enough to worry about them.
Other possible carcinogens include rubbing lead all over your body and licking 50 year old paint.
Of course, the actual magnitude of effect is so monstrously different that it'd almost seem dishonest for someone to claim this in a vacuum, especially in the face of the several decades of research, several thousand studies, several hundred animal tests, all of which have found no actual proposed chemical route of cancer generation from aspartame.