Okay since I haven't seen it said here so far. Aspartame is being classified as "a possible carcinogen". The reason for that is observational data. We have observed an increase in obesity related cancers in people who also have daily intake of aspartame. This observation is 1.15 times higher than the background rate (people not having daily aspartame and developing obesity related cancers), so that is what is prompting the classification. There is additional research into if this connection is casual (Synchronicity) and it seems that there is some initial evidence to suggest this is more than just a casual connection.

Remember back to science class. We science by making an observation, posing a hypothesis, testing that out, and then drawing conclusions from it. This move is one of the first steps after the observation part in the political sphere. Science is just making an observation, however, governments are free to move in lock step with those observations or wait till science gets a bit further along in the process. Really depends on the flavor of government we're talking about, but the important part is that whole section of the equation is distinctly NOT SCIENCE.

So that said, where everyone else is chiming in on with aloe vera and what not is the classification the International Agency for Research on Cancer (IARC) is placing aspartame into. This is a political group that moves in step with science research. This group has four levels. 1 - You will get cancer, 2a - Pretty likely you will get cancer, 2b - Maybe you might get cancer, 3 - You will not get cancer. Aspartame is being moved into 2b.

There is still a lot of research left to go about the links between aspartame and cancer. For example, aspartame seems to only cause cancers typically related to obesity, so is it the cause or are obese people just selectively drinking it? This is what I referred to at the start as a casual connection. BUT, there is a whole process before we can technically say "YES". So that process must happen first. But there's going to be people who attempt to say "well yes, obese people get obese cancers, duh" and initial evidence suggests that there is a bit more that we ought not to just hand wave away.

As for what you SHOULD do. You should do what you feel is best. If it puts your mind to ease to nix aspartame from your diet, you should most absolutely do that. But yes Coke Zero has the exact kind and chemical make up of sweetener that Diet Coke has. So if that is the thing you are trying to excise, Coke Zero is not a respite.