Does Splenda and Aspartame, etc. Make You Fat? What about the Natural Alternative, Stevia?

I wanted to talk about artificial sweeteners today because I've noticed that there's a lot of confusion and misconceptions revolving around these non-caloric sweeteners. Artificial sweeteners and the huge list of products sweetened with them are marketed to you relentlessly as “healthy foods” or “healthier” than sugar or corn syrup sweetened products. But are they really healthy or do they cause all sorts of health problems