This is a topic I've wanted to address for some time now, however there's a TON of information out there and i'm skeptical of reliability.
My trusty Nutrition Action Healthletter just included a quick synopsis and I figured i'd paraphrase. More to come when I have some extra spare time.
Acesulfame-potassium (honestly, I'm not even sure what this is) - Tests conducted in the 70's were mediocre although one suggested it may result in an increased cancer risk in female rats.
Aspartame (NutraSweet, Equal) - Two recent rat studies show it may slightly increase cancer risk. New studies should be done.
Saccharin (Sweet N' Low) - In animal studies it has caused cancer of the urinary bladder, uterus, ovaries, skin, blood vessels and other organs.
Stevia - It appears to be safe although it needs more independent testing.
Sucralose (Splenda) - It appears to be safe although there hasn't been a ton of independent testing. It also apparently isn't as natural as ads have implied.
What does this all mean? Honestly, i'm not sure. Moderation perhaps?