Prayer is useless, an empty thought in your mind that you hope will affect something happening in this world. The truth is, you are the maker of destiny, not prayer. If you want to help someone going through hard times, just being their friend and confidant will make a difference. People who believe prayer works don't get that reguardless of what they hope for, people will do what they want, feel how they want, and make their own paths and decisions. For instance, you can pray for the people in Syria and the violence to stop all you want to, but that's not going to change the fact that Pres. Assad is determined to keep killing his own people everyday. So no, you shouldn't pray for people you don't know- Its selfish, because It just makes you feel better about witnessing the suffering of others, and it doesn't make any difference whatsoever!
Avoiding the religious references, you surely must realize the importance of something as simple as a thought in your head. Thoughts will have an effect upon the body and through that upon ones environment.
I remember as a kid being around a nervous dog that would tend to frequently snap at me, I was told to "not show fear" as the way to avoid being bitten (by those that were also around this animal and never ever bitten). I didn't quite realize properly how to do that but I understood the general principle.
Later in life while working with horses I had one horse that would freak out when walking over a spot in some cement where the line of the form was at. Most others had no troubles leading this horse over that line (some did, though). The trainer indicated to me that I was giving indication of nervousness or tenseness to the animal unbeknownst to me. I told him I was acting the same as always but he showed me how he had no problems and explained that horses (as most animals -- including people) can pick up the subtle indications that we give off (a tightening of grip on the lead or increased tension on the lead, stiffening of the arm, subtle change in pace, turning to look at the animal or the spot, etc). He said you can try to adjust these things but often you don't realize which it is and when you try to adjust you only end up highlighting focus on them or causing something new. He taught me that the best way was to picture yourself walking the horse over the line and the horse acting fine. He said to "tell yourself the horse will walk over the line fine and without any problems" while picturing it. This had a stunning and noticeable effect and improvement was immediate (although it wasn't initially complete but noticeably better until the "freak out" sessions practically disappeared).
I also used 'visualization techniques' to improve my three point shooting from poor to where I could hit 70% or more of these shots from a set and unguarded position. I used visualization to break sticking points in weight lifting to overcome a problem with benching more than 300. I am sure others have had experience with such things.
As I mentioned, people also notice such things. I am not saying that this is the mechanism of prayer as I believe prayer has its own source, but I am sure this does lend to solutions. Whenever you focus mentally on something or visualize an outcome your body does not know the difference and works as it can to conform to this image or to accept it. Your body can even develop neuromuscular pathways as a result of simple visualization. Your brain can also be prompted to get out of the way with its doubts and uncertainties. The subject is more complex than that, of course, but the proof is evident that "thoughts in your head" do have a significant effect upon yourself and your surroundings.