M.D. Anderson in Houston, one of the largest cancer hospitals in the world, has been a hotbed of such research. One trial studied the outcomes of 25 patients with pancreatic adenocarcinoma, one of the worst cancers to be diagnosed with, who were taking curcumin and nothing else -- as in no chemotherapy! Researchers found cancer growth stopped in 2 patients. Actually a large liver tumor in one patient shrunk by 73% in their estimation. (Other tumors in that patient did however grow.) You can read about the trial here. The actual manuscript describing the trial can be downloaded off the McCormick Spice Institute's website.
Many cancer survivors find this news hopeful. You can see some survivors' reactions to the trial here. One survivor observed that pancreatic cancer rates in countries where people eat a lot of turmeric is low (e.g., India and Thailand) and high in countries with low consumption (e.g., the U.S.). Here's one piece of evidence to support that claim (LINK).
One final note. I liked that this trial was done in people. Many trials, like this one from UCLA demonstrating how curcumin in combination with a conventional chemotherapy fights head & neck cancer cells (news report and study), are performed in petri cells or mice. Sure, we can extrapolate from conclusions in cells or mice. But the best evidence that something works comes from studies done in people.