Stevia is widely used by people all over the world as a sweetening agent and is said to have a pleasant taste. The FDA has looked at the evidence on safety and reported the following:
Stevia leaves are a native product in Brazil and Paraguay. The extract, stevioside, has reportedly been approved for use in foods in Brazil and Japan. The product is used in these countries as a table-top sweetener in virtually all food commodities and as a flavor enhancer in such products as teas. Stevioside is reportedly 250-300 times sweeter than sugar and contributes no calories to the diet.
Though it can impart a sweet taste to foods, it cannot be sold as a sweetener because FDA considers it a food additive. “The safety of stevia has been questioned by published studies”, says Martha Peiperl, a consumer safety officer in FDA’s Office of Premarket Approval. “No one has ever provided FDA with adequate evidence that the substance is safe.”
Under provisions of 1994 legislation, however, stevia can be sold as a ‘dietary supplement,’ though it cannot be promoted as a sweetener. With regard to its use in foods, stevia is not an approved food additive nor affirmed as ‘Generally Recognized as Safe’ (GRAS) in the United States. Available toxicological information on stevia is inadequate to demonstrate its safety as a food additive or to affirm its status as GRAS. However, with regard to its use in dietary supplements, dietary ingredients, including stevia, are not subject to food additive regulations.” 
There has been another issue raised in animal testing – how it may affect normal hormone production. At least one study suggests it can lower testosterone in males. 
We have two other considerations from a practical standpoint; one, it can be very expensive. Second, although most people who have tried it say they prefer the taste to artificial sweeteners, there have been no well controlled studies indicating any weight loss among those using stevia. In the March 2001 issue of Consumer Reports, foods prepared with Stevia were reviewed and found to be lacking in taste or significant nutritional value when compared to other sugar substitutes.
: U.S. Food and Drug Administration; FDA Consumer, November – December 1999 “Sugar Substitutes: Americans Opt for Sweetness and Lite” by John Henkel
: J Ethnopharmacol 1999 Nov 1;67(2):157-6. Effects of chronic administration of Stevia rebaudiana on fertility in rats. Melis MS