American Journal of Physiology

Well, it depends on if your goal is to burn fat.

This study took 10 overweight dudes (average waist size was 41) and either fed them or had them fast before a 60 minute brisk walk on a treadmill. The feeding was about 650 calories, two hours before the exercise, and the fasting lasted 12 hours.

*Side note*
This is sort of a tangent, because the calories were all they were comparing with fasting, but have a look at what they fed the non-fasters...

...the meal included white bread (Brace’s thick white), cornflakes (Kellogg’s cornflakes), semi-skimmed milk (Sainsbury; British semi skimmed milk), orange juice (Sainsbury; 100% pure squeezed smooth orange juice), spread (Unilever; I can’t believe its not butter), jam (Sainsbury; strawberry jam) and sugar (Sainsbury; British white granulated sugar).

Really!?

Makes you wonder how strong the results would be if you compared fasting with say, oh I don't know, a diet that actually contains nutrients and not just sugar. I wouldn't be surprised if the meal was enough to gain more weight than they lost in the exercise.

Anyway

The researchers measured metabolic rate and fat tissue before and after the workout and found some interesting results.

"…feeding prior to acute exercise affects post-exercise adipose tissue gene expression and we propose that feeding is likely to blunt long-term adipose tissue adaptation to regular exercise."

In other words, after eating fat is too busy responding to the meal to respond to the exercise, which prevents you from using it as fuel.

Sciencey details

The expression of two genes, PDK4 and HSL, increased when the men fasted and exercised. The rise in PDK4 likely indicates that stored fat was used to fuel metabolism during exercise instead of carbohydrates from their most recent meal. Also, HSL typically increases when adipose tissue uses stored energy to support increased activity, like exercise. Two good things if you're trying to burn fat.

More importantly, both PDK4 and HSL decreased when the participants ate before exercising.

Takeaway: Exercise in a fasted state might provoke more favorable changes in fat tissue. If you eat before you exercise, your body will burn through the carbs from the meal instead of any stored fat, making it difficult to lose weight.

Fasting 12 hours before a workout should help you burn fat as an energy source, instead of the food you just ate. That might also mean that the food you eat before exercising is immediately burned as fuel, so eat up if you don't have excess weight to lose.