Here's a write-up I did on Stevia a while back, which includes scientific studies. I've never come across any studies that have even eluded to such a possibility.

I went ahead and did a quick review of study abstracts on PubMed and didn't find anything indicating a link between stevia and cancer.

Perhaps these people are thinking of Aspartame (NutraSweet)? This stuff is very dangerous and is well-known to cause tumors.

In my opinion, if this kind of information is being put out to the general public, it's probably because Stevia is a completely healthy and natural sweetener that can't be patented, while Aspartame (NutraSweet and Equal), Sucralose (Splenda), etc. can cause serious problems, including liver and kidney failure, nervous system disorders, and even death. Yes, death.

The video Sweet Misery is a well-done documentary that explains the truth behind NutraSweet's big money and lies and what it is really doing to your body.