Currently, there are eight approved artificial sweeteners in the US. The most popular or commonly used are sucralose, aspartame, stevia, and saccharin.
Although these sweeteners have been approved by the FDA, there's a ton of controversy regarding their safety. Animal studies have shown increases in cancer risk and kidney failure. Keep in mind, the animals were given and unbelievably high dose of sweetener, far more than the average human consumption (and we are much larger).
We advise that you enjoy artificially sweetened items sparingly. Consistent and/or long-term consumption of artificially manufactured substances should be avoided.