Benson, Dusek and Hibbard did what most consider the most thorough study in the area. It was in Volume 151 Issue 4 of the American Heart Journal, you can see the abstract here http://www.ahjonline.com/article/S0002-8703(05
)00649-6/abstract but there is a paywall for the article. I can't find a copy of it for free online but you can probably get a print version at a well stocked library.
There are a ton of others studies as well but they are, for the most part, scientifically flawed. Usually from improper sample sizes and methodology or just media hype mis-interpreting the actual studies (or authors like Larry Dossey dramatically misrepresenting certain studies). They range the gamut of for and against, but few to none are really repeatable.
Also, to clarify, the lack of impact or negative impact has really only been shown in prayer for others
. Ones own prayer does show some evidence of a positive effect, generally it seems to be the same effects one can receive from different forms of meditation.