The best exercise for burning calories is the one you will actually commit to doing that will get your heart and lungs pumping moderately harder for an extended time. This type of exercise is called aerobic or cardiovascular exercise, and many activities are considered aerobic if done at the right intensity for 20 to 60 minutes.
Gyms usually have a several machines for this purpose, such as treadmills, elliptical machines, rowers, bikes, vertical climbers and stair climbers. You can also participate in a class that will get you moving, such as spinning or step.
Outdoor activities such as hiking, running, biking, in-line skating and swimming are great ways to burn calories and enjoy some fresh air. Sports such as tennis, squash and basketball are fun ways to burn calories with a buddy, and the game itself can make the time seem to go by faster. All of these activities will burn at least 400 to 800 calories or more per hour when performed with medium to high intensity.
The most important thing to remember is that the actual activity isn't as important as the intensity and length of time you do it. To burn maximum calories, you must get your heart and lungs working hard enough that it's slightly uncomfortable (but not impossible) to talk and continue at that level of intensity for 20 to 60 minutes. If you aren't starting to sweat and breath a little harder after a proper warm-up and 5 to 10 minutes of activity, turn up the intensity by moving faster or, if on a machine, adding more resistance.
If you are new to exercise, don't forget to check with your doctor to make sure you are healthy enough for moderately intense exercise.