This is a controversial question on car-related boards. Here's what I've learned and observed over the years. Take it for what it's worth.
First of all, the official position of the government and most consumer organizations is that there's no advantage to using gasoline of a higher octane rating than what the manufacturer recommends. Unfortunately, that's not always the case. But even more unfortunately, there are too many variables for any answer to be right all the time.
First of all, as all pilots know but most people don't, the "octane" rating is actually an anti-knock rating, and nothing more. So unless you're driving your car in a manner such as would induce detonation, using higher-octane fuel than recommended would provide no benefit -- if that were the only difference. But it's not.
I used to have a client that was a primary gasoline supplier that mixed the gas that many different companies pump. No matter the brand or grade, all gasoline starts with the same stock. The only differences are the additive packages. His company added the additives to the basic gas and supplied it to the various labels. What he told me was that in reality, there are more differences between grades of fuel at a given label than just the octane alone. But they vary based on location, time of the year, the label, and the upstream supplier.
One important difference is how much energy the fuel contains. Around here, 89-octane fuel actually contains slightly more energy per gallon than either 87-octane or 91-octane fuel because of the way it's blended. I forget the actual numbers, but the gas that arrives in the big truck only has two octane ratings. (I think they're 85 and 89, but I could be wrong.) Everything else is a blend of those two, plus ethanol.
Whatever the exact numbers, the way it works out is that 89-octane has the least ethanol by volume, which means it has the most energy by volume because gasoline is much more energy-dense than ethanol. To increase the octane over 89, they add ethanol, which reduces the tendency to detonate, but which also reduces the energy density.
The higher energy density of 89-octane over 87-octane is enough to provide a slight increase in MPG, but it wouldn't be enough to make it worth the cost for most people. But for some people it does. The difference is whether one's driving is such that it is likely to induce detonation.
Where I live, in the hilly Catskills, I get between five and ten percent better fuel economy on 89 than 87 in local driving, but no measurable improvement over 89 or when driving on an interstate. I can also take most hills one gear higher with 89 than I can with 87. The reason is that when the engine starts to knock, all cars' ECUs take actions to stop it. The most common compensations are to retard the spark, enrich the mixture, and downshift (on automatic-transmission cars). All of these actions reduce fuel economy, but are necessary to prevent and correct knocking.
By using a higher-octane fuel, you make the car less susceptible to knocking, hence the ECU doesn't have to apply inefficient corrections as frequently. Whether it makes any measurable MPG difference depends on the terrain, the way you drive, how much weight you're carrying, whether you're pulling a trailer, and many other factors. But the point is that if your driving is such that it tends to induce knocking, then using a higher-octane fuel will usually increase MPG by reducing the frequency of anti-knocking corrections. If not, then it won't.
In a nutshell, the best answer to the question of whether or not it's worth it to use 89 in a car that can use 87 is "It depends." If you live on a prairie and drive like your maiden aunt, then probably it's not. If you live in the mountains, frequently pull a trailer, and/or drive like Mario Andretti, then quite possibly it is, depending on the price difference
What I usually do is quickly calculate the price difference while I'm at the pump, and if it's 10 percent or less, I choose the 89-octane. If it's more than 10 percent, I choose the 87. I'm actually spending a bit more than I'm saving at a delta of 10 percent, but the car runs better going up the hills. That counts for something, too.
Rich