Does a mirror help a near-sighted persion see at a distance clearer? A near-sighted person without eye-glasses can not clearly see things at distance.
If he takes a photo of the things at distance, he can see the things from the photo much clearer, because he can place the photo much closer to his eyes.
If he turns his back at the things at distance, and holds a mirror close to his eyes in a position so that the mirror reflects the things at distance behind him, will he see the things much clearer than if he looked at the things at distance directly?
 A: With a flat mirror, it would be worse.  The distance from eye to object is the distance without the mirror plus twice the distance from eye to mirror.
With a convex mirror, it is even worse than that. 
With a concave mirror, the answer depends on the curvature, the severity of myopia, and the distance to the mirror.
A: Assuming the mirror has no curvature then things would not look clearer.
You have to think about the image as it is being projected, our eyes doesn't perceive reflected image as being at the point of reflection but rather perceives the image as being a set distance from our eyes. 
To clarify if you imagine your eyes couldn't look at anything but the mirror it would almost be like looking at a window, thus the distance the the object is still the same distance away from the viewer and glasses would be required to resolve the image. 
A: I am suffering from myopia (nearsightedness). I tried the same (with out wearing my lens), result was I could see things clearer in front of me than when I saw the same things in the mirror.  
The below figure shows image formation for a person suffering from myopia.
 
Lens in our eye is more convex at its back than in front. For simplicity lets assume it to be convex lens.  As our eye lens is of small focal length, we can assume every object to be at infinite distance. When the object is at infinite distance you get image formation as shown below.

Whether you see the object in a mirror in front of you or see the object far away from you, we can assume light rays to be incident from infinite distance (because of small focal length of our eye lens).  
Visible light emitted or reflected from objects around us provides information about the world you see.  
When you see things behind you in the good mirror it will be able to reflect only $85-95$% (aprox) of light falling from it. When you see same things directly, you will be able to see greater percentage of reflected light. Thus, you will see sharper image.
A: does a flat transparent glass make near-sighted people see farther? the answer to this question is the answer to yours.
A: Edit: Reading other people's answers, I forgot to mention I assumed a flat mirror.
Excellent question, but the answer is no. The reason is because the object (in the strict optics meaning) in the case of the photograph is actually on the paper whereas in the case of the mirror it is still at the same place, far behind: the rays of light coming from it are reflected on the mirror but still require tuning from the eye muscles to get the focal point right (the eyes are in fact sort of a tunable lens with a detector similarly to cameras). 
I would recommend you draw a diagram of the light rays coming from the edges of the objects into the eye for both cases to get a better idea.
Example
As an example, consider the following: if the mirror has dust on it, try looking first at the dust and then at an object that the mirror displays behind you. You will have to strain your eyes to focus on the dust, which proves that what the mirror displays is not actually at its surface (the image, again in the optics strict sense, is behind the surface of the mirror).
A: Not necessarily. It depends on where the image is formed from the mirror. Depending on the radius of curvature (assuming spherical curvature) the image ould form anywhere, but the person would want it to form on their retina. You can calculate this using the mirror equation
$\frac{1}{d_{0}}+\frac{1}{d_{i}}=\frac{1}{f}$
Where $d_{0}$ is the distance (from mirror) to the object, $d_{i}$ is the location of the image (w.r.t to mirror), and $f$ is focal length.
So it does not matter how close the mirror is to the persons face, it only matters where the image is formed.
A: A mirror presents a reversed world, as viewed through a 'virtual eye'.  That is, if you were to place your eye at the place where the eye's image would be, the rays of light would still be unaltered.
But the 'virtual eye' would suffer the same effects as the real eye: an image in the mirror is still out of focus for a person whose distant vision is out of focus.
It should be noted in passing, that optometrists use a reflection of the eye-chart for eye tests.  That is, the eye-chart is reversed, and behind you.  You look in the mirror and see it in the correct sense, but essentially twice across the room.  In this way you can get a 20-foot distance inside a 10-foot room.  
I used to have one of those mirrors with magnification on one side.  This does not really help.
With a spyglass (say a pair of binoculars or a monocular (half of a binoculars)), it is possible to adjust the focus at the eye peice that you can see unaided things far away.  I carry one of these in my dillie, that i might read the bus numbers without glasses (i normally wear reading glasses going out, since these are more suited to business and shopping).
A: Any optical system that can form an image on the retina is well suited. The eye has deficiency of few dioptres and if the optical system can provide them at the right distance one will see clearly.
A mirror with curvature can also be used however it wound not be convenient for every day use. It would be sort of adapted mirror telescope (regular telescope is afocal system). 
