Scientific Studies Aspartame has been found to be safe for human consumption by the regulatory agencies of more than ninety countries worldwide, with FDA officials describing aspartame as “one of the most thoroughly tested and studied food additives the agency has ever approved” and its safety as “clear cut.”
When the European Commission’s Scientific Committee on Food evaluated aspartame (pdf) they found over 500 papers on aspartame published between 1988 and 2001. It has been studied in animals, in various human populations including infants, children, women, obese adults, diabetics, and lactating women. Numerous studies have ruled out any association with headaches, seizures, behavior, cognition, mood, allergic reactions, and other conditions. It has been evaluated far more extensively than any other food additive.
When new rat studies by the Ramazzini Foundation in Italy (link) appeared to show an association with tumors, the European Food Safety Authority examined Ramazzini’s raw data and found errors that made them discredit the studies. Their updated opinion based on all the data available in 2009 said there was no indication of any genotoxic or carcinogenic potential of aspartame and that there was no reason to revise their previously established ADI (Acceptable Daily Intake) for aspartame of 40 mg/kg/day. (You would have to drink over 8 liters of Diet Pepsi in one day to go over the ADI.) Studies have shown that actual consumption is well below that limit.
People who are absolutely convinced they get adverse effects from aspartame have been proven wrong. For instance, the New England Journal of Medicine published a study (link) of people who reported having headaches repeatedly after consuming aspartame. When they knew what they were consuming, 100% of them had headaches. In a double blind crossover trial, when they didn’t know what they were getting, 35% had headaches after aspartame, and 45% had headaches after placebo.
Saccharin (Sweet n' Low) was on California's list of chemicals known to cause cancer for several years. The label was added to comply with CA law. Saccharin was removed from the list in 2001[link] because the few studies that showed a link to cancer had been disproved. I do not know of any other artificial sweeteners that were on the list at any time.
In the case of Saccharin, the biochemical pathway that turns it into a potential carcinogen, only exists in rats.
Whether or not artificial sweeteners lead to diabetes or weight gain isn't the issue here. The issue is that artificial sweeteners have not been shown to be carcinogens. So lay off. I am going to drink my Diet Dr. Pepper and you can enjoy your high fructose corn syrup.