I found a post on The Reiki Digest that Gloria A. Gronowicz performed a vigorously designed three-year study on applying Reiki treatments to test-tube cells. The study was designed so the application of Reiki did not involve touching the tubes, heating them, or manipulating them phisicaly in any way.
The results showed (against her expectations) that Reiki had no effect on cancer cells, "but that the process improved bone cell growth by a statistically significant percent. Skin and tendon cells also grew under the Reiki regimen.".
The study was performed by the University of Connecticut Health Center and financed by the US National Institutes of Health Center for Complementary and Alternative Medicine, and apparently* published in the Journal of Orthopedic Research.
*) "apparently" means that I could't find or access the study dirrectly (but then again, I didn't want to pay for access on the CCAM website).
Later Edit: Following a discussion on reddit, It seems there are some points of this study that were contested as part of peer review (as I said in the discussion, the statistics part is a bit above my statistics-fu and I'm not willing to put in the effort to understand the issue, so I'll take the affirmations in the critique at face-value). Please take the conclusions of the study with a grain of salt though.