Here’s a good case study of how scientific information gets distorted. This article has sources, which is a little unusual (but they are not links, probably to discourage you from checking them out for yourself), but look at how they're used...
Here’s the conclusion of the first study:
"Although our findings preserve the possibility of a detrimental effect of a constituent of diet soda, such as aspartame, on select cancers, the inconsistent sex effects and occurrence of an apparent cancer risk in individuals who consume regular soda do not permit the ruling out of chance as an explanation."
In other words, inconclusive.
The second study is on rats and has significant results. It's a single study and not a meta-study: http://www.ncbi.nlm.nih.gov/pubmed/16507461
The third one, well, there's no third one, it's the same link as the first one.
So what does the MassReport.com article say about these articles?
"a can of diet soda daily increases leukemia (cancer of the bone marrow, blood) in both men and women by 42%."
Well, that's a lie. Here's what the abstract really says:
"when sexes were analyzed separately with limited power, neither regular nor diet soda increased risk of leukemia but were associated with increased leukemia risk when data for men and women were combined (RR for consumption of ≥1 serving of diet soda/d when the 2 cohorts were pooled: 1.42; 95% CI: 1.00, 2.02)"
So it's very likely a statistical fluke: the data simply doesn't make sense, from the authors' own opinion. That even higher risks of cancer were found in men with regular sugar soda (that is ignored by MassReport) doesn’t improve the trust one can put in the results. Additionally, scientific results come with error bars (the CI interval that is in the complete abstract and that MassReports conveniently ignore), that make the results even more dubious. This is why the conclusion from the authors of the study are that it is inconclusive.
But wait, there's more: MassReports tells us
"What concerns us even more is how Aspartame is created. According to an article by The Independent, it has been confirmed by both a Monsanto spokesperson and a Monsanto source that the Aspartame creation involves genetically modified bacteria."
It concerns you even more than a risk of cancer that it's produced from GMOs? Why would that be? Could it be that you have no idea what you're talking about? It so happens that a very efficient way to produce simple organic molecules and proteins is to trick living organisms into doing the work, usually by manipulating their genome. There is no magical property that gets added to a molecule by the modified organism. The molecule is strictly indistinguishable from another copy that would have been obtained through more classical chemical synthesis. In fact, I suspect that the traditional chemical industry is way more harmful to the environment...
So what to make of that? Well, there's enough data on rats, and enough uncertainty on people to cast a sinister shadow on these products. I'm avoiding sodas myself (both sugar and sweetener-based), and prefer water and juice to them. That's an easy decision to make: water is, for sure, the best drink you can have health-wise. It is however a little too early for that class-action lawsuit against Coca-Cola. More science needs to be done...
The other obvious conclusion is that you should not take your science news from clickbait web sites. Always take the time to dig a little deeper and look at the actual research, it's usually more accessible than you think.