I rarely ask anyone to spot me in the gym. If I'm doing a heavy bench press, I'll set up in a cage and position the safety rods so that they can "catch" the bar before it cleaves through my chest if I fail to press it up. This isn't ideal, but I don't trust spotters.
Usually, a spotter is a guy you interrupt while he's taking a break between sets to come help you on yours. He doesn't really know what he's doing, and he's not much in the frame of mind to do it right anyway. He thinks his job is to help you lift the weight you're using at all costs, so he'll put his hands on it too soon, or help you lock out your elbows when you should be doing it under your own steam. All this does is prevent you from doing the work yourself, and that reduces the results you get. Worse, it can give you a false sense of confidence. You might bench 250 one day with a spotter, and then come back the next week and have to use 240 because the spotter wasn't there to pull the bar up.
The following are some of the official guidelines on spotting as prescribed by the National Strength and Conditioning Association (NSCA).
The main responsibility of the spotter is the lifter's safety. The secondary responsibility is to help you get extra forced repetitions, but we'll discuss that more below.
Exercises that should be spotted include the squat, front squat, shoulder press, bench press, and lying triceps extension. In other words, any time the bar is on your back or collar bone, or when you're pressing a weight over your head or face. That's it! There's no need to spot curls--that's just cheating.
When spotting a dumbbell bench press, PLACE YOUR HANDS NEAR THE LIFTER'S WRISTS. I know everyone pushes the elbows but this is bad. It provides too much assistance and is dangerous--if your friend's wrists bend inward and he loses control, he could drop the weights on his face. And your hands being on his elbows could even help that happen!
When spotting the barbell bench press, use an alternating grip (one hand palm down, one palm up). This gives you better control.
The spotter and lifter need to communicate and agree on how the set will be done before the lift. I prefer to tell the person how many reps I'm going for and then tell him not to touch the bar/dumbbells until I say ok, or it looks like I'm about to die. This usually makes it pretty clear that I don't want assistance unless I'm really unable to complete the lift.
There are different schools of thought on this, and certainly a spotter can be used to help you perform forced repetitions after you can't complete a clean one on your own, but most experts I've spoken to recommend using the spotter for that purpose rarely, if at all. Besides being dangerous even with the help of a spotter, doing forced reps or similar high-intensity techniques can very quickly lead to burnout. To make progress, you only need to lift a little more weight or perform one more rep than you did the week before, and trying to force that much more out of your body makes it very difficult to keep that pace up.
If you're benching, a "liftoff" can be helpful. This is where the spotter(s) help pull the bar off the rack and position it over you to begin the set. It helps you keep your tight position and not lose the arch in your back. But beyond that, I prefer to use spotters for safety alone.
Of course, you can always use a spotter to "motivate" you through a set by yelling mantras such as "light weight, light weight!" and "it's all you, man". But then it had better really be all you... man.