Sometimes. If the conditions are right.

However, if you ask the question, "Which gives me the most ice for the water," the answer is cold

Here's the problem with the convection argument above: Why doesn't the hot water reach equilibrium when it reaches 4C? As the water gets cooler, the convection currents become weaker and when it reaches 4 degrees Centigrade the once hotter water would be subjected to the same problems of the cold water. Of course here would be where the conduction argument above would work best, but what if there isn't ice on the shelf? What if I had just defrosted my freezer?

The largest factor in the hot water freezing faster (also known as the Mpemba effect) is, in fact, evaporation. If you put water in the freezer that is 99C and water that is 20C, the hot water will evaporate much of it's volume. With simple math, it's easy to see that less mass of water means faster freezing. When talking about ice cubes in a tray, there is a larger surface area to volume ratio then say, a bucket of water.

There is another factor of impurities in the water. Heating water releases gasses that otherwise lower the freezing point. Cold water retains all of these, and in common experiments can cause inaccurate testing.

But then again, we're talking about making ice cubes.

I suppose if you want to be purely technical, water that is colder will freeze faster - all other things being equal. But if you want to make your ice cubes in a slightly shorter amount of time, put in hot water. But remember - they just might be ice slivers by the time they're done!