Water is recycled through nature automatically. And there are always rivers to collect rainwater, treatment plants to make it drinkable.
Everyone who thinks that fresh water is unlimited should do a quick search of their local aquifer levels; it's not an unlimited supply. Each year, a certain amount of water falls in our regions, and (usually) we use more water than we get. This means that our aquifers are being depleted.
We have a natural budget, but most places are well exceeding it. Sometimes for stupid reasons, like watering the lawns during the day and the like.
To answer the OP: because we like to save water, we usually flush every third or fourth pee, but we always flush after a poo (and before, if the water is yellow). This means that we flush, on average, at least half as much as other people do.
As well, because the water treatment process required that toilet water be 'aged' for a certain amount, not flushing each time actually takes some strain off of the local waste treatment plant (because we're introducing more aged waste water than normal). So, it's also easier (in our micro way) on our tax dollar. Therefore, not flushing each time allows us to: more efficiently use our aquifer water, reduce our water bill, and reduce our strain on the infrastructure.