You might want to read this Wikipedia entry: https://en.wikipedia.org/wiki/Observable_universe#Size. The simple answer to your question is that if you find a galaxy from which light took 12+ billion years (not 14; the estimated age of the universe is less than that) to reach us, that galaxy was 12 billion light-years from us when that light was emitted; it would be much farther away today.

I think the correct answer is different: if those galaxies are 14 billion l-y from us now, when their light left them they were less appart from us, because space itself has expanded in the meantime. Therefore, their light has not taken 14 billion years yo reach us, but a lot less.

In the same way, if light reaching us now started coming very near the origin of the universe (for instance, light in the cosmic background radiation, which started around 13.5 billion years ago) the current distance run by that light is not 13.5 billion l-y, but about 3 times more (about 40 billion l-y) due to the expansion of space.

Simiar to previous answers, the way I visualise this situation is to assume the galaxy was very much closer to the Milky Way at the time the photons we are collecting now were emitted. However, the expansion of the Universe led to a situation analogous to running up an escalator going down - the photons took much longer to reach us than they would have had the Universe not been expanding.

In fact, as the expansion of the Universe is accelerating, it is even possible for galaxies that are sufficiently far from us today to emit a signal towards us which never actually reaches us. If you like, you can set up the governing equations for the problem with distances increasing as t^0.67 (before dark energy was important) or as e^(t/11Gyr), dark-energy dominated (last 5 Gyr or so). Then, the velocity of a photon towards us is c - the rate at which the remaining distance to Earth expands. This will need to be solved by separation of variables. It is possible for the distance remaining to always increase, meaning the photon will never reach Earth. Sad times :(

Manuel and Indranil: I wasn't guessing my answer. I provided a factual statement about relativistic cosmography. Allow me to elaborate. Please see also this stackexchange discussion: http://physics.stackexchange.com/questions/57402/size-of-the-observable-universe

Light that took 13.7 billion years to reach us traveled exactly 13.7 billion light years from its point of origin. This is not a measurement of coordinate distance, however, since we are comparing the location of two points in spacetime (ours and the light emitting object's) at different times. (light emitted at t=t1, r=13.7 Gly, and observerd at t=t2, r=0.)

Consider a coordinate system in which we (the observers) sit at the origin, at rest. That means that our spatial coordinates do not change; we were also at the origin 13.7 billion years ago. Therefore, the coordinate distance between us and the light emitting object was 13.7 billion light years at the time the light ray was emitted. (The coordinate distance between events marked by t=t1, r=0 and t=t1, r=13.7 Gly.)

What this distance is today (i.e., the radial coordinate of the object at t=t2) depends on the rate of expansion. Without repeating what can be read elsewhere, stuff that was 13.7 billion light years from us when it emitted light that reaches us today would be about 46 billion light years from us today.

Manuel: in your answer you say, "if those galaxies are 14 billion ly from us now"... but that's not what we infer from the redshift. We observe that it took 14 billion years for their light to reach us, i.e., that they were 14 billion light years from us back when the light was emitted, not their present-day distance from us.

Indranil: In your answer you mention acceleration. It is indeed true that acceleration can result in a distant source that was once able to send us a signal to be no longer able to do so. But the reason is simply that these sources will be traveling faster than the speed of light relative to us and thus, would no longer form part of the observable universe.

Answer to V. Toth:

I still disagree with you. No redshift could show us a set of galaxies that were at 14 Gl-y from us when they emitted the light. Since the universe started about 13.8 gigayears ago, the light of no object beyond 13.8 Gl-y can have reached us by now.

In fact, the highest red-shift we can ever detect is that of the cosmic microwave background (CMB), which started towards us about 13.5 Gyears ago. This redshift amounts to about 1100. Everything beyond this cannot be seen, because the universe was opaque at that time.

The farthest galaxy (quasar) whose redshift has been detected has a redshitf of about 11. This means that it is much nearer away from us than the CMB. That is why I assumed that Daniel was referring to galaxies 14 Ml-y from us NOW. The light from these galaxies would have taken much less time to arrive to us.

Manuel: as I indicated, I wasn't expressing a personal opinion. I was providing factual information about how FLRW cosmology works, which anyone can verify by looking at the resources for which I provided links, studying relevant textbooks, and using a calculator.

You are of course correct when you say that "the light of no object beyond 13.8 Gly can have reached us by now." But you forget that this limit, 13.8 Gly, is about the distance of the object at the time it emitted the light, not its distance at the present day.

A redshift of 11 is not that much nearer than the CMB. The light travel time for z=11 using more or less standard cosmological parameters is 13.24 Gyr. For z=1100 (CMB), it's 13.67 Gyr. The comoving distance for these two is 32.2 vs. 45.7 Gyr. (See http://www.astro.ucla.edu/~wright/CosmoCalc.html). So the light travel time is only 3% less, the comoving distance about 31% less for that z=11 galaxy than it is for the CMB.

Addendum: Manuel, re-reading your comment, I think you are correct in your last paragraph. The actual article referred to by Daniel in his question describes objects from which light has taken 9 billion years to reach us. While this is by no means the most distant object ever observed, 9.2 Gyr actually corresponds to a z = 1.45 and a comoving distance of ~14 Gly.