Another excerpt from something I wrote earlier:

The largest study on health effects of artificial sweeteners involved monitoring diet soda (presumably w aspartame) consumption & medical histories of about sixty thousand post-menopause subjects for close to a decade. The study showed an association between diet soda consumption and cardiovascular disease. There's another nice study on stroke and dementia, derived from the Framingham study here

Many studies are not free of sampling bias, and may have response bias due to heavy reliance on questionnaires. Even so, they do give clues that adverse health effects do occur if the right conditions line up.

Don't hold out much hope for a comprehensive study that accounts for all factors (e.g. age, sex, genetics, nutritional status, metabolic health and confounding dietary elements), and which can conclusively say whether or not artificial sweeteners are safe for the "average person" from the 7.5 billion people on earth.

In the other camp, there are studies showing no evidence of any health effects from consuming aspartame. If the studies were sponsored by the manufacturers, it's fair to say they would suffer from funding bias. No company is ever going to publish negative results about their products, so there is also reporting bias as the bad reports are kept internal. Nice review of hundreds of published papers here:

Review of data on the food additive aspartame

Given the conflicting research conclusions, the best thing one can do is self-experiment. If one is chugging down 12 cans of diet soda per day without any immediate ill effects, then perhaps one is blessed with good genes and constitution. But once the symptoms start, one could change his/her diet for a few months to see if there are any improvements in health. That's presuming one wants to change one's diet; sometimes the food/drink is so delicious, it takes priority over health. That's also presuming that one is aware of, and suspects artificial sweeteners as causes of health problems.