Improperly adjusted headsets often go unnoticed: many peoples' bicycle's headset is a little loose, sometimes too tight.
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!
Step 1: Assessing Your Headset
Like I said, optimally you want a buttery smooth headset (yes, that is a pseudo technical term!) that offers no resistance to turning the handlebars (i.e. isn't too tight) and isn't loose. I'll mention here that determining if your headset is loose/tight is the same if you have a threaded or threadless headest, but adjusting the different types of headsets it is different. This instrucatble is for adjusting a threaded headset (there are nut-looking things between your headtube and stem that you can put a wrench onto).