The calculation in the other answer is rather naive. I haven't done the calculation myself, but there are a few things to consider. First of all, lighter wheels mean more than just lower overall vehicle weight. Advantages are:
- lower overall vehicle weight: lower inertia of the car
- lower weight of the wheel (rotating part): lower rotational inertia
- (probably) different aerodynamic behavior
- lower unsprung weight
Weight distribution in the wheel also makes a huge difference. If the weight is more to the center, there's even less rotational inertia. Therefore, smaller diameter wheels are better than large diameter wheels! Clearly then, saving 10 kg in weight on wheels has a much higher impact on fuel economy than saving 10 kg by removing the backseat or something. A (itself quite naive) calculation suggests a factor of 1.5 difference, based purely on the rotational inertia.
You're especially going to notice the difference when accelerating and decelerating a lot (because that's when weight matters), so in city driving your savings will be higher than in constant high-speed highway driving (where drag matters).
A test was conducted on a racetrack with 3 different wheel configurations, documented here. They also did a road test to measure fuel economy, but the main goal was better lap times. Obviously, the lighter wheels yielded better lap times.
Unfortunately though, the road test actually registered worse fuel economy for the lightweight wheels. There's a few things that explain this result, having to do with the fact that this test aimed to optimize the car for lap times, not fuel economy. Those are the wheel size (the lightweight wheel had a larger diameter) and different tires (the stock tires were optimized for low rolling resistance). The stock wheels were already light as well, 20.5 pounds, while the lightweight wheels weighed 17 pounds, so the difference wasn't that major. There may also have been a difference in driving style. I wonder what the results would be with identical wheel size, the same tires and controlled driving conditions.
However, it's still interesting to note that the differences in fuel economy were quite measurable, about 2%. It's hard to determine what that would mean for real-life driving situations, but I could imagine a set of carefully chosen wheels saving a few tens of bucks on a yearly basis. That'd still mean you'd have to drive the car for at least a couple of years to pay for the wheels (assuming you receive the same amount when selling the car), but the lifespan of most cars probably makes the investment worthwhile.
NB: I'm not thinking about an expensive set of wheels here, I bought a set of less than €300 for my wife's compact car, with the same diameter as the original set. They obviously aren't magnesium wheels though, those are way more expensive.