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.