Although an improperly adjusted headset won't cause a fire or catastrophic bicycle breakdown, it'll wear out the headset faster and make controlling your bike a little more difficult. Plus, I usually ride 'no hands,' and having a buttery smooth headset that's not too loose is pretty critical to the sans hands riding.
Moreover, by checking the headset you can find many possible problems with your bike (not only headset problems). Much of this instructable is dedicated to diagnosing the problem, which simultaneously diagnoses other potential issues with your bike.
This is actually a really easy thing to check for, and it takes less than a minute to do. After you get the hang of it, properly adjusting a headset only takes a few minutes to do. Don't be scared by all the steps - I'm just trying to be as clear and thorough as possible!