You should always drive like you're about to run out of gas. In other words, coast before you brake. By coasting, I mean no brakes, no gas. On a short street, in a parking lot or in a neighborhood, there's no need to apply too much gas. If you see that you're going to have to stop (Stop sign or red light in front of you), immediately take your foot off the gas, coast, and cover the brake as you prepare to slow down.
When driving behind other cars, you should immediately take your foot off the gas and cover the brake whenever you see brake lights or a turn signal on the car (or cars) in front of you. Doing this significantly reduces your chances of rear-ending the vehicle ahead of you.
When you only need to slow down a little bit (for example, coming from a 45 MPH zone into a 35 MPH zone), just lift your foot off the gas pedal. The car will automatically slow itself down - just quit feeding it gas. No need to slam on the brakes.
As a general rule, while driving on the interstate, don't use your brakes unless absolutely necessary, such as coming upon a wreck or a serious traffic jam. If you keep at least two seconds behind the car in front of you, you should never have to apply brakes, unless the vehicle in front of you hits their brakes.
If you're gaining on a slow moving car in front of you, let off your gas and cover your brakes. The wind resistance against your car at high speeds will help slow you down quickly. Although the two second rule is probably best, a quick rule of thumb is: If you're going over 55 and you can read the license plate of the vehicle in front of you, you're too close.
Every time you hit the brakes when you don't need them, you're grinding down your brake pads, and you've just wasted the gas you were using to accelerate. If you see a stop sign ahead, think about what you're doing - drop off the gas for a moment before you have to apply your brakes. Make sure if you turn that you have your turn signal on at all time.