Good idea, but that only harms one person…Maybe if you setup an institution and sold your services…or just picked people up randomly off the street to be tortured and let a few ‘escape’ to spread the word of your institution (to create fear in the general population, see)
I’d definitely start a religion. Give yourself up to Darrylism. I’d make up a fairly compassionate set of commandments but throw in a couple of silly ones just for the hell of it. I wouldn’t do the ascetic thing and my disciples would be hot young women. The sacrament would be beer. Hell, if I died in the process, I’d still have my 2000 years of fame.
I would not like this to happen to me. I couldn’t heal everyone, and how would I be able to judge who deserves healing most? And besides that, there are other moral conundrums, too. Like worrying about saving someone you shouldn’t have. Or saving lots and lots of people and helping to contribute to overpopulation. Basically, I don’t want to be God.
My first stop would be to my best friend who has non-Hodgekins Lymphoma that is not responding well to current (or prior) treatment.
Everything else would just be icing on the cake.
Oooh… I like this very, very much. GREAT idea!
I would try to make a very good living off of it and heal as many people as possible. As soon as possible, I would set up a strong compound and invite family and friends to live in or near the compound. I would attempt to generate enough revenue to sustain all of this. I would do what I could for those who cannot pay, but I would ensure I have time for myself and ensure people understand my powers were limited and I needed to rest. I would hire a martial arts coach to both teach me self-defense and to help protect me. The medical benefits I could offer would obviously be top notch.
I have some sick friends I would visit early. Can I cure Alcoholism? How much can I do for old age?
I would do what I could and at the same time try to get a medical team and scientist together to study my ability and see if it could be developed in others. My BIL & SIL are a Medical Doctor with a strong research background and a Doctor of Biology devoted to research. I would count on them to help build a good team. I know where I could find a good nursing staff. Both my sisters and my niece are nurses, two RNs and a LPN.
I would give special very discount rates to veterans. Always keeping in mind that one person could only do so much.
Should I develop these powers I would be recruiting some help from fellow dopers.
I would probably eventually go as mad as Willy Wonker. 
Jim
Hrm.
So, by your example, injuries are definitely healable. What about genetic conditions that are literally part of a person’s normal life? Someone born with a genetic disorder, for example, may be injured, but that’s what they’re like… does the ‘power’ refuse to work on them because they were ‘supposed’ to be that way?
Is it involuntary? Suppose I trip and land on a sick homeless man lying sprawled in J. Random doorway. Is he going to spring back to youthful vigor with no further effort on my part?
If the answer to both is ‘no’, then there’s some serious potential here.
I’d heal my family and friends first, secretly. They don’t have injuries, per se, but several (most?) of them have one or another genetic condition that I would love to see corrected. Hell, myself included (diabetes).
Next, I’d try to find a reputable, honest, and discreet doctor (or several). This may take a while. Once I’ve located him/her/them, I’d demonstrate my power in secret, before they know my identity, and offer them a deal in which I would heal patients who really needed it (meaning, there’s no possible cure available, or there’s not enough time left), let them take the credit, and they pay me for the service. I’d need to be on their salary somehow, but I could have a ‘front’ job as a computer technician or whatever. They let the secret slip, they lose out – I’ll simply stop performing.
I don’t want to be rich or famous. I just want my debts paid off and enough money to live on comfortably. I don’t particularly CARE about my ‘fellow man’, so I doubt I’d feel any inclination to help EVERYONE.
It couldn’t last forever, of course; someone’s bound to talk. But a couple years collecting a sizeable salary would be enough, and there’s no way to prove it was me. Hell, after a couple years, I could go back to school and get an M.D. myself and run the whole show. That might be the way to go, heh.
Someone’s bound to point it out, so I’ll clarify: yes, I feel morally and ethically justified in deciding who lives and dies, based solely on my own judgement, and possibly on the judgement of those I trust (which comes back to the same thing, sort of). That may make me a callous bastard (or whatever), but I’m okay with that, thanks.
To answer the questions about the limits:
No bringing people back from the dead.
Yes, you must touch them.
You can learn to control it so that it’s always voluntary.
Yes, you can cure genetic disorders.
Yes, you can cure psychological diseases and addictions.
You can cause someone to regrow a missing limb or organ.
You can cause an old body to repair itself at least to a certain extent.
And you can’t use it on yourself (just to be more difficult).
Edited to add: You can’t do things like making an average person into an Olympic sprinter by improving them genetically.
Televangelism.
Hey, if it works for people without the ability to heal…
Well, first, I’d cure Ivylad’s back and neck and hernia. Then he could have that morphine pump under his skin removed.
I’d probably stay quiet, or at least arrange for protection and agents so I could insulate myself (a la Kyle in The 4400) from the mobs.
There are all sorts of implications. Would I have to take the Hippocratic Oath, and swear to heal anyone, regardless of circumstance? There’s only so much one person can do, and when faced with the choice of two people on the opposite side of the globe, one a child dying horribly of cancer, the other a serial pedophile dying horribly of cancer, and I can’t save one in time to save the other…well, do I have the right to condemn the pedophile to death? Or do I focus on the one right in front of me and not worry about the rest?
If I had this power I would’ve used it on my Aunt to cure her Breast Cancer. Hell I’d cure all women who have/had Breast Cancer. I miss her dearly and wish she was still here. 
So I would use it to cure all women.
I’d try and keep my power secret. I’d find and cure a rich and connected patron who would arrange for discreet introductions to other rich and discreet people every now and then. And in the course of my normal job and life, I’d ‘press the flesh’. Discreetly.
Consider the ramifications of such a power being made public: it’s clearly a supernatural power, therefore God (or Allah or Amerterasu…) exists. Atheism would disappear. I’d be the target off all religions, and some of the nuttier types would probably try to kill me.
Help, but undercover.
Only folks who can’t pay for regular medical treatment.
And deny having the ability, or optionally claim to have it, & give the skeeviest come-on for money I could dream up, to drive off the cynical.
I certainly wouldn’t want people to know I had the power to heal, because of the kinds of things that Sonia Montdore mentioned. Few things would be worse than ending up in some kind of research lab or held hostage.
I would be as sneaky as possible. I’d go to hospitals wearing scrubs so I’d blend in. (St. Jude’s would be the first stop on my list.) I’d quietly slip into wards and heal as many people as possible, healing those with painful burns and other horrible ailments first-- in case I’m detected and have to make a run for it. And I’d try to do it while people are asleep so they wouldn’t figure out it was me.
I wouldn’t feel comfortable with charging people, especially since my powers don’t “cost” me anything.
Can this power also be used to heal animals?
Nah, it wouldn’t be that hard at all, if the power was as described in the OP. A BIG hospital might have a few thousand patients, many of whom aren’t in any sort of dire need. If you prioritize right and just go from room to room, it would be about as demanding as being a mailman.
I’d try to spend as much time as I could healing people. In this far-fetched scenario, that’s the only ethical choice.
Does this power also let me give explosive diarrhea to politicians telepathically? No reason…
Me, I’m a cynic. I figure if I showed up tomorrow with such an ability, people would assume I’m some kind of Messiah. There’s got to be an angle for that — sure, one healer probably wouldn’t do much good in the world, but a Messiah could change the way people act for thousands of years.
I like this idea, but a good cleric needs to have lots of buffing spells and some offensive spells as well, not just a bunch of heals. (Yes, I do mostly play clerics or cleric/wizards or cleric/sorcerers, they make it easier to solo if you can get them to a high level.)
Sure.
And no, you can’t give people illnesses this way, politicians or no!
I’d just go to the upcoming Democratic National Convention and start shaking hands like crazy.
…
Actually, I’d go to the local Shriners Hospital and heal those kids.