"All things being equal, you will burn more calories by running an hour than walking an hour. It is true that walking a mile will burn more calories than running a mile -- although it takes longer to do so. When you run a mile, you're burning mostly sugar, or carbohydrates, which is how your body gives you fast energy in bursts. When you walk a mile, it gives your metabolism time to switch from burning carbohydrates to burning fat." "How many calories you burn depends on a variety of factors such as fitness level, metabolism, weight and the intensity of the workout. 'Larger people burn more calories than smaller people, particularly with activities like walking or stair climbing where they have to carry their own weight,' says Robert McMurray, professor of exercise and sports science at the University of North Carolina at Chapel Hill." [sources http://my.webmd.com/content/article/3079.883 and http://www.ivillagehealth.com/interests/healthy/articles/0,11299,165839_125472-1,00.html]

As opposed to editing my answer, I'll add a different one in attempts to address the surprising amount of user response I received on my answer :). [I also read a very good answer in Runner World magazine incidentally, similar to this one so hopefully this brings up the right points]: "Running requires substantially more energy per unit of distance. Several factors contribute to this. Shall we start with entropy and the second law of thermodynamics? Eh, maybe not. How about aerodynamic drag, which increases with the square of the speed? Probably not something you need to worry about unless you've really been hitting the steroids. Here's something a little more relevant: Analyses of the biomechanics of walking vs. running suggest that walking is a more efficient gait except at higher speeds. The crossover point is somewhere around 5 mph, varying with the individual. At that speed, walking and running are equally efficient. Below the crossover point, running is less efficient, apparently because you lose energy absorbing the impact of the ground with your bent knees. Above it, walking falls behind because of the awkwardness of the racewalking gait. Gait is the critical issue, incidentally--running speed is irrelevant. Subtracting out the energy required just to keep you breathing, you'll use about the same amount of juice finishing a marathon in two hours or four. To return to our main point, running consumes more calories per unit of distance than walking. For a person who weighs 70 kilograms (about 154 pounds), walking at 5 kilometers per hour (3.1 miles per hour) consumes 50 calories per kilometer, whereas running at 10 kph (6.2 mph) consumes 78 calories per kilometer. When you begin a workout your body is metabolizing carbohydrates, but as the minutes tick by you start burning fat--at minute 50 of light exercise, you're chugging along on a 75/25 fat/carb mix. Sixty percent of your maximum aerobic capacity (reached at roughly 75 percent of maximal heart rate, which is generally calculated as 220 minus your age) is optimal for fat burning; as exercise becomes increasingly strenuous you start burning more carbs. Some have seized on these facts to claim that sustained low- to moderate-intensity exercise is a better way to shed flab than going all out. The point is hotly disputed; I merely note that for the significantly overweight, walking can be easier on the heart, joints, etc." [source http://www.straightdope.com/columns/050121.html] Well still not as good an answer as in the Runner's World magazine... :) Wish I had the article.