As a driving instructor, I often ask people what are their "pet peeves" about other drivers; a common reply is that other drivers don't signal turns and lane changes. How many times do you see drivers who do not signal? Or worse, drivers who signal a right turn but turn left? Other times, especially with vehicles whose signals do not self-cancel (trucks and motorcycles in particular), you'll see the oblivious driver cruising down the road with a signal still blinking when the turn was perhaps miles back down the road! It is important to pay attention!
Sometimes, drivers deliberately don't use turn signals . They think that if they signal a lane change before they start it, on a freeway for example, that other drivers will prevent their lane change by closing the "gap." That happens sometimes, but remember that courtesy is contagious too. Just as often, other drivers WILL make room for you if they know you want to make the change, and quite often (especially in freeway merge situations) they may want to change lanes to the right for an exit at the same time you are merging left into the lane. If both of you are signaling, it is very easy to coordinate the movement safely. NOT signaling in situations like that is exceptionally dangerous, and the resulting wreck often includes several vehicles -- not just the ones that didn't signal.
Most of us believe that traffic law says signals are always required, but that is not always true. In some states, the law requires a signal only if your change in movement will affect another nearby driver. If you are on a lonely highway at 3:00 AM, and there is no one else around for 50 miles, it may not be required for you to signal a turn! However, the reality is that most of us drive in places and times when our changes and turns do affect others, and from a defensive driving point of view, I recommend you always signal turns and lane changes -- and doing so creates a habit. This is one area where being on auto-pilot can be a good thing! If you always signal, then you are one step closer to being predictable which is a benefit to the other drivers on the road with you. And everyone gets to feel all warm and fuzzy!
Be careful not to send the wrong message when you signal. Make sure you send clear information. For example, if you are approaching an intersection, and you intend to turn right immediately after the intersection into a service station, be careful not to signal too soon. Other oncoming drivers may interpret your signal that you intend to turn AT the intersection rather than beyond it, and they may turn left in front of you. Finally, use your signal before you start the turn or a lane change! It's not of much use if you wait until you're halfway through the turn before you use the signal!