Yes.
- Levin & Chatters, Journal of Aging and Health -- "Religion, Health, and Psychological Well-Being in Older Adults" (1998):
These findings provide mixed support for the three study hypotheses, with Hypothesis 1 (an association between organizational religiosity and health status) farinb best. In general, results suggest that (a) religious involvement is moderately and significantly associated with health status and psychological well-being; (b) these associations withstand controlling for effects of key sociodemographic constructs such as age, race, and gender; (c) these associations emerge across a variety of indicators; and (d) results are present, though inconsistent, across samples drawn from three large-scale national probability surveys conducted in the 1970s and 1980s. (SOURCE)
This is a meta-analysis of several surveys from the 70s and 80s, so the data may not be representative of society today. There are some caveats provided in the discussion, as well, such as that one set of data did favor the correlation between religiosity and health, but not religiosity and psychological well-being.
- Abdel-Khalek, Mental Health, Religion, & Culture -- "Happiness, health, and religiosity: Significant relations" (2006):
Based on the self-rating scales, the current data provide strong evidence that, among a large sample of Kuwaiti Muslim undergraduate students, religious people are happier.
...the main predictor of happiness was mental health. So, the self-rating of religiosity came as a predictor of happiness, but to a lesser degree. (SOURCE)
- Ross, Journal for the Scientific Study of Religion -- "Religion and Psychological Distress" (1990):
The positive emotional function of religion has been well accepted, but the evidence has not been conclusive. Furthermore, research has rarely made explicit comparisons to persons who claim to have no religion. Using a representative sample of Illinois residents (and controlling for sociodemographics and willingness to express feelings), I found that the stronger a person's religious belief, the lower the level of psychological distress. (SOURCE)
This is an old study, and featured in a journal with a title that may reveal an agenda. I can't be sure, but at least want to mention it. I would be thrilled to see a footnotes for the statement that "the positive emotional function of religion has been well accepted..." That might provide many more sources for this claim.
- Levin, Social Science & Medicine -- "Religion and health: Is there an association, is it valid, and is it causal?" (2002):
This paper reviews evidence for a relationship between religion and health. Hundreds of epidemiologic studies have reported statistically significant, salutary effects of religious indicators on morbidity and mortality. However, this does not necessarily imply that religion influences health; three questions must first be answered: “Is there an association?”, “Is it valid?”, and, “Is it causal?” Evidence presented in this paper suggests that the answers to these respective questions are “yes,” “probably,” and “maybe.” (SOURCE)
- Chida, Steptoe, Powell, Psychotherapy and Psychosomatics -- "Religiosity/Spirituality and Mortality" (2008):
The results of the meta-analyses showed that religiosity/spirituality was associated with reduced mortality in healthy population studies... but not in diseased population studies. (SOURCE)
I realize this is not a psychological benefit, but still found it interesting, and it appears (from the comments) that your original question may have included requests for examining correlation between religion and other benefits as well.
- Davidson et al., Psychosomatic Medicine -- "Alterations in Brain and Immune Function Produced by Mindfulness Meditation" (2003)
We report for the first time significant increases in left-sided anterior activation, a pattern previously associated with positive affect, in the meditators compared with the nonmeditators. We also found significant increases in antibody titers to influenza vaccine among subjects in the meditation compared with those in the wait-list control group. Finally, the magnitude of increase in left-sided activation predicted the magnitude of antibody titer rise to the vaccine. (SOURCE)
I was actually forwarded this study a few weeks ago and list it here to show that while the literature suggests that religion does have a positive effect on health and psychological states, so does mindfulness/meditation. Davidson also gives a talk entitled, "Be Happy Like a Monk" -- one can watch it or request the transcript HERE, if interested.
Just for some counter-points, I thought I'd list these:
- Effects of participation in Alcoholics Anonymous (AA) (LINK):
Affiliation with AA after treatment was related to maintenance of self-efficacy and motivation, as well as to increased active coping efforts.
I offer this simply to illustrate that (as Levin's paper about causality also aims at), it might not be merely religion that improves psychological conditions, but the aspects of social bonding, support, being accepted, having an important goal, a common purpose, etc.
- Paul, Journal of Religion & Society -- "Cross-National Correlations of Quantifiable Societal Health with Popular Religiosity and Secularism in the Prosperous Democracies" (2005):
In general, higher rates of belief in and worship of a creator correlate with higher rates of homicide, juvenile and early adult mortality, STD infection rates, teen pregnancy, and abortion in the prosperous democracies (Figures 1-9). The most theistic prosperous democracy, the U.S., is exceptional, but not in the manner Franklin predicted. The United States is almost always the most dysfunctional of the developed democracies, sometimes spectacularly so, and almost always scores poorly.
I add this, as these individual effects of religiosity may be measurable, but perhaps religiosity on the societal level, or at least various forms of it, are not correlated in the same manner, at least with external/societal benefits.
As always, correlation does not equal causation. While there is evidence supporting the claim examined here, the fact that it doesn't seem to matter which religion it is, that AA may have such benefits, and that individual benefits doesn't scale as a society makes me want to look further. I'd be particularly interested in the Levin paper above, for the abstract also contains this:
Third, alternative explanations for observed associations between religion and health are described.
Finding this and other papers looking at similar things might be quite interesting, unless the only question of interest here is purely about religion/health/well-being. Personally, I'd like to know the underlying mechanisms as well, as the benefits of religion might be reducible to lower factors that could prove useful.