Does psychic healing work?

In my opinion, It can.  However it is not always as straightforward as tapping your head with a wand.

First whether you can be healed depends on your karma.  You may not be ready to release the karma but if you are the healing can be almost instantaneous.

Your attitude is a factor.  If you ask to be healed but don't believe you can be then chances are strong that you won't.  This smacks of positive thinking but nevertheless is an important factor.  It amounts to being open to the energy working for you.  You are in control of your destiny and if you want to block the healing you can.

I had a healing done on my enlarged prostate and the results were almost immediate.  Within a day my symptoms were gone and have not returned.  Since this is a medical impossibility and since the symptom reduction was demonstratable I'm now a believer.

 Morever, Psychic healing does, sadly, not work. 

While it would be lovely if thinking nice thoughts, or waving hands around, or even touching people in a special magic fashion did have this capability, decades of research into this area have gradually pushed it out of the mainstream of science. This is not because anyone is trying to censor it, or "big pharma" are suppressing it, or anything like that. 

Psychic healing research has been marginalised as it has not demonstrated as effective. 

One of the other answers refers to the William Bengston "laying hands on mice" study. He is a sociology professor rather than a medical researcher, which is not ideal, but that is OK - he's had it peer-reviewed, right? 

Well, the journal he published in was the Journal of Scientific Exploration, a publication that focuses on UFOs and astrology, so it is perhaps not the most uncritical forum for this work. But presumably they do peer-review, as they say. Perhaps the study is good? 

Sadly, there are numerous issues which even as a layman are obvious in the methodology used to carry out the study, the lack of careful controls in place being a  particular issue, but there are others concerns, documented here: The Effect of the “Laying On of Hands” by William Bengston. At the very least, this study needs to be replicated with the myriad methodological issues rectified. 

But more seriously, the Cochrane review (the gold standard for knowing what works and what doesn't) of therapeutic touch for minor wounds found: 

"That trials do not show therapeutic touch to be beneficial in healing wounds from minor surgery and that the trials are at high risk of bias."

As i know that this Cochrane review is not ONE study, as Craig Weiler seems to think. It is a review of studies, in this case of four other studies. Cochrane reviews are how clinicians and scientists know what seems to work, according to the best available evidence. 

Further, if it wasn't clear enough, I have read the study: it contains methodological problems including relaxing protocols as it went along, and including letting participants take the mice home (!) and contains various subjective (and unevidenced) claims in the narrative around how certain participants were or were not "skeptics". 

And as for the other studies, which Craig says show "good results" for psychic healing:

• Astin et al's conclusion: "The methodologic limitations of several studies make it difficult to draw definitive conclusions about the efficacy of distant healing". Published in a mainstream journal. Does not show good results for psychic healing.
• Leibovici is interesting, published in the Christmas issue of a mainstream journal known for carrying somewhat unusual studies in said festive issue. It's worth reading the letters that followed it up: Page on bmj.com as it includes Leibovici's own response, explaining his trial to have been more about methodology, statistics and commentary on whether you should test impossible treatments in RCTs. Many people missed this subtlety, or the fact the paper was a spoof, but not everyone, as one letter writer put it: "a thought provoking paper but may just prove the power of statistics, not of prayer."
• Krukoff et al was published in a mainstream journal and described itself as a pilot study only, and includes the following conclusion: "No outcomes differences were significant". Does not show good results. We'll come back to this one shortly.
• Radin et al does show "good results", but is published in a non-mainstream journal. Hopefully it will be replicated in a mainstream journal. I'm not aware of such a replication. Until then, mainstream science will understandably pay it little heed. Worth a quick read of Radin's Wikipedia entry, too: Dean Radin
• Krukoff et al's follow up in the Lancet has this conclusion: "Neither masked prayer nor MIT therapy significantly improved clinical outcome..." Again - not good results.
• Benson et al, in a mainstream journal: "...intercessory prayer has no effect on complication free recovery..." and worse, "certainty of receiving intercessory prayer was associated with a higher incidence of complications". So not just not a good result, this was a bad result.
• Masters and Spielmans say, in their abstract "The effects of distant intercessory prayer are examined by meta-analysis and it is concluded that no discernable effects can be found." Again - not a good result for psychic healing. 
• Radin et al, published in Explore, (not a mainstream medical journal), and a small study. Neither of these invalidate it, but it needs to be replicated, preferably in a mainstream journal.
• Schlitz et al: also in Explore, a moderately positive but fairly small exploratory study with aforementioned reservations. And even this study notes in the background: "clinical trials to date have provided ambivalent support for its [distant healing intention's] efficacy"

So of those nine papers, we have only three that are positive, published in alternative journals, and one of those is with caveats. Of the remaining six, which were published in mainstream journals, we have four that are not good, one that is actively bad, and one that was essentially an intentional spoof.