Absolutely, It's a very common phenomena and a long existing problem. Recently, RSC organized a competition for explanation of this effect. I am posting a link where the final 10 entries are given out of 22000:
http://www.rsc.org/mpemba-competition/shortlist/
I discussed once it with my Prof. and he explained it in a nice way, ''First of all, It 's kinetics, not thermo. Imagine many people who have to sit on chairs very well plced (organized) and two situations: a)people who can freely move very fast to unoccupied chairs versus those who are slow and somehow tight together with ropes and who also have to move to unoccupied chairs: guess which group will win the race.''
Thanks a lot Dr. Pimiskern and Dr. Mohammad. The phenomenon is truly amazing.
Well it is not freezing faster, but it CAN freeze faster.
Usually it is called the Mpemba effect (although there have been reports of similar phenomena since ancient times).
I think there is no final agreement on the how the process exactly takes place, but the an easy and plausible explanation is that the lower temperature water will tend to freeze faster as a "block", while the warmer water will tend to freeze a "single layer" at the top and this further isolates the water mass.
So in a sense, the lower temperature water will ALWAYS freeze faster (until becoming a single ice block), but the warmer water may create faster an ice cube with liquid water inside.
Here you can find a nice paper with some deeper insights:
http://www.rsc.org/images/nikola-bregovic-entry_tcm18-225169.pdf
But this effect is not alone, since the "opposite" also holds, namely, lower temperature boilers can sometimes vaporize water faster than higher temperature boilers (Leidenfrost effect)
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