Question: I've run a number of races, and there are almost always a number of water stations. I don't usually stop for water on the short races, but I'm not sure how long of a race I should do that for - when should I start drinking water? How much and often should I drink it?

Answer: 
Hydration when racing has a lot of variables, all of which need to be taken into consideration for longer races - which I would say is anything longer than a 10k:

* difficulty of the course (hills, headwind, altitude)
* temperature and humidity
* and your acclimatization to those weather conditions
* your effort, this is somewhat of a double edged sword: run fast and you're done quicker, run slow and you're out there longer, and often you'll be out in the warmer parts of the day more than the early finishers.
* your body: everyone sweats different amounts. Some don't drink much during a 1/2 marathon, some drink a liter or more.
* for longer races, your nutrition intake also adds a fluid component: you need water for your body to digest the nutrition.
* pre-race hydration: it's not uncommon for racers of >4 hour races to adjust up their electrolyte and hydration in the days leading up to a race.

First - try to do a sweat test in an environment as close as you can to the race, and get a good idea of what you generally need, and then consider the other variables.

At the end of a race you will almost never hear people saying "oh dang, I drank too much", but go by the medical tent after a marathon, and you will see racks of people wishing they had taken hydration more seriously.
It depends on the race and the weather.
At a marathon i stop at almost every station and grab a glass of water and have sip. 
Its better to hydrate in small sips from time to time.

With a bit of practice you can even learn how to drink while running so you don't lose to much time at the stations.