Water is too cheap, which is why people don't care about wasting it.
There is also the fact that if you don't use it, it just evaporates, floats around as a cloud for a while, and then drops back to earth again, as rain. The water cycle, believe it or not, still works in the same way it did when you were a kid in elementary school. So really, there's no real shortage of water.
Except when there is:
It is impossible to predict which year will be a drought year. In the 1990s, when I lived in/around Philadelphia, there were at least two summers where you could be forgiven for wondering what happened to summer, because everything was brown. It didn't rain for three weeks straight, once--and given the average temperature of a Philadelphian summer, that's a big strain on plant life.
It is becoming even more difficult thanks to the weird climate changes we are all experiencing. Drought and famine in Africa. Drought and famine in India. Glaciers melting, Venice under water. Northern Europe caught in a web of freezing cold. More powerful hurricanes.
The problem is not that water actually runs out. It is that it runs out where people live. But it's not like you can keep it, either--evaporation occurs, no matter what.
So why "save" water?
1) Why not? If you're not using it, why run it? It's a profligate waste of money and resources.
2) Those "just a few bucks" you save--any little bit helps if you're struggling. Turn off the faucet, fix those leaks, and you'll breathe just that much easier.
3) Peace, quiet, and no green streaks. When I was in college I lived in an apartment where the bathtub's faucet leaked all the f*cking time. Eventually we were able to summon a groundskeeper to fix it, but by that time there was an irremovable scum of green stuff staining the white tub, marking where algae had grown along the trace of the water. Dripping faucets drive me nuts in general.
4) Water damages. See #3 about green scum. But a drippy pipe can cause floorboards and cupboards to rot, and those cost a helluva lot more to replace than calling the plumber to fix the leaks.
5) Save your skin. Washing too often dries out your skin, and washing your hair too often sucks the natural oils that give it shine right out. I wash my (long) hair every other day--it's oily--which is just about right.