Even if most artificial sweeteners on the market are generally considered safe * in moderate quantity * if you look close enough almost all of them have been associated with health problems [...]
Even for Stevia there are legitimate concerns: in a study [http://www.ncbi.nlm.nih.gov/pubmed/8962427] the researchers found that intestinal bacteria in rats (but they found the same bacteria in human colon) transformed steviosides (the active ingredient in Stevia) into a compound called steviol, which is toxic, causing an increase in mutagenic DNA damage. The "safe" dosage seems to be no more than 1.8 mg per pound of body weight.

The only harmless artificial sweetener seems to be erythritol:
http://www.ncbi.nlm.nih.gov/pubmed/19632091
http://www.ncbi.nlm.nih.gov/pubmed/16277764

But besides health concerns there are other effects involved in artificial sweeteners consumption:

1) overcompensation for expected caloric reduction. People say: "hey, there is no sugar in my soda, so I can eat more pizza"

2) an appetite boosting effects caused by the sweet nerve sensations from our tongue that is not compensated by the appetite suppressing effects of the caloric food entering our system: this usually results in overeating

In Artificial sweeteners and the neurobiology of sugar cravings Yang writes: "Whether due to a successful marketing effort
on the part of the diet beverage industry or not, the weight conscious public often consider artificial sweeteners “health food”. But do artificial sweeteners actually help reduce weight? Surprisingly, epidemiologic data suggest the contrary. Several large scale prospective cohort studies found positive correlation between artificial sweetener use and weight gain"
The full article here: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2892765/pdf/yjbm_83_2_101.pdf