Yes, absolutely - by all means do everything you can to recycle and reuse your wasted water. This is good ecological practice.
"Collect your rainwater and use it flush your toilets, or, even better, water your lawn and garden."
But realize that both situations, as you explained it and as I explained it, coexist. Both you and the original poster touched on the truth (though you are in error about some minor points):
"The sky gives you free water, and you watch it run down the street." - Original poster
"And most rainwater is not reclaimed by the state or city or whatever, it runs into storm drains and then into streams, creeks, and oceans." - Booner
As the administrator for a municipal stormwater program, we deal with the water cycle on a daily basis. If you remember from middle school science class, the water cycle is the way our most precious finite natural resource is continually refreshed and recycled. Let's take groundwater as a 'beginning' point (you could pick any step of the cycle to begin, as it's a circular process). Groundwater feeds surface water bodies like rivers, oceans, lakes and streams. It also feeds water wells. Surface water bodies undergo continual evaporation into the air. Water is drawn up into the atmosphere, where it eventually is condensed into clouds. These clouds are also fed by transpiration, which is the release of moisture by living things like trees and plants. The clouds release their water unto the earth via precipitation, which is what you're catching in your rainbarrels. This stormwater then passes through vegetation or porous material like gravel (permeable surfaces) and infiltrates back down into the ground water table, recharging the aquifer to start the whole process over again. Stormwater also performs another important function in acting as runoff, which recharges surface water bodies.
The function of a city or state's water program isn't to actively reclaim this naturally recycling water. Our job is to keep it clean and flowing, so that it can perform the function that it was intended to do. That's where I was saying that if there were significant quantities of rainwater being caught and diverted away from recharging the aquifer, it would have a deleterious effect on life as we know it. Imagine your water well. It's drilled as far down as it took for the driller to strike the water table. If water is continually being drawn out of the aquifer and not replaced, these water wells will fail. It is in this respect that naturally occuring stormwater is considered a 'resource of the state', and as such, its use is regulated.
Of course, in the quantities that the original poster is proposing, most states/communities would wholeheartedly support the environmental intent of this purpose. We should all be good stewards of our most valuable resource. Reclaiming water from treatment plants is proving to be another important way to conserve this resource.
Here are a few facts that most people don't know:
Water is constantly recycled. There is the same amount of water on Earth now as when the Earth was formed.
80% of the total surface of the Earth is water, in one form or another.
97% of that amount is water in its liquid form.
2% of that amount is frozen and unusable.
Only 1% of the Earth's water is suitable for drinking.
If 66% of our bodies is comprised of water, including 75% of our brains, then we have an incredible personal interest in making sure that there is enough clean and potable water to go around. Just food for thought...