Does 1 kg weigh as much as 1 liter of water?

Answer

This question is actually about physical units: the kilogram is the unit of mass, just as the meter is the unit of length and the second is the unit of time. A liter is a derived unit, namely a unit of volume defined as one thousandth of a cubic meter.
So you can in no way say that a kilogram is a liter, just like you cannot say that a kilogram is a second or a meter.
It is also important to know that the mass of a body is not equal to its weight. The weight of a mass of a mass of one kilogram depends on where you measure that weight. For example, Frank De Winne is weightless in the ISS, but not massless. A mass only gains weight in the presence of a gravitational field. But on the Earth’s surface, mass and weight yield the same numerical value if they are both expressed in kilograms, because we have defined it that way historically. I assume that you are situated “on the earth’s surface”, so that we can simply speak of weight on the earth’s surface, expressed in kilograms.

In parentheses, on the difference between mass and weight, see for example:
http://www.technopolis.be/nl/watkunjedoen/indekijker/exhibits%20vd%20week/weeg Scale.htm
http://ourworld.compuserve.com/homepages/gene_nygaard/weight.htm

A liter of water has a weight of one kilogram. Why ? Simply because we have defined it so historically. See about this: http://nl.wikipedia.org/wiki/Liter

However, one liter of something does not always weigh one kilogram. Weight is the product of specific gravity and volume.
Take, for example, pure lead: the similar weight of lead is 11.35 grams per cubic centimeter. Now one liter is a volume of 1000 cubic centimeters. One liter of lead therefore weighs 11.35 kilograms. A real heavyweight in Mendeleev’s table is Plutonium, with a specific gravity of 19.8 grams per cubic centimeter. One liter of plutonium therefore weighs 19.8 kilograms.

A kilogram of feathers does indeed weigh as much as a kilogram of lead, but a kilogram of feathers does take up a much larger volume, so a much larger number of liters, than a kilogram of lead. After all, the specific gravity of springs is much lower than that of lead. This is also an application of weight = specific weight times volume.

(By the way, I have sinned in this answer (mea culpa) by expressing the specific gravity in grams/cm³instead of in kg/m³ . But yes, we are used to that in everyday life…)