^ He is right.
But I see these questions so much, so let's really address this properly. I know this is long, but bare with me if you really care to know.........
Octane ratings are a measure of resistance to detonation. The higher the octane rating, the less likely the fuel is to detonate and make an extra hole in your block. Most higher compression, VTEC and turbo cars require extra protection from detonation due to the higher cylinder pressures seen during the compression stroke.
Feeding cars that require atleast 91octane 89 octane gas usually won't start breaking things because the knock sensors will see it coming and retard the ignition timing or turn down the boost, reduce HP and most likely throw a CEL making you and your engine enjoy life alot less.
When you have a car that requires 87 octane or better, an Integra LS for example; they will run perfectly fine without any detonation on that gas. If you were to feed it 91 octane, nothing would change. The car would still run fine, there would still be no detonation, and you just emptied your pocket for more expensive gas for no reason. Doing things like advancing ignition timing and raising the compression ratio could cause knock which would necessitate the need for a higher octane gasoline to prevent this.
There are a few exceptions with the technology going into newer cars, not many of which are Honda's.
A stock Dodge Neon SRT4, for example, lets the ECU control boost and shoots for a power target. If you were running 91 octane, the ECU may increase boost to 16psi and pull a little ignition timing to meet it's power goal. If you were running 94 octane, it may reduce boost to 14psi and advance the igntion timing and still reach the same target power. The benefit of the higher octane would be a mild increase in fuel economy.
Another, but different, scenario would be on a Subaru WRX. The Subaru WRX ECU will read the knock sensor to determine if timing needs to be retarded to prevent detonation just like most modern cars. But unlike most other cars in the world, the Subaru will actually use the knock sensor readings to probe the limits, not just to reduce power under knock. If you were to run 91 octane in a WRX, the ECU may reduce timing to the point of staying just outside the threshold of detonation. But if you were to fill up with 94 octane in the same car, the ECU will actually see the zero knock feedback and advance timing beyond the norm and probe the limits of the knock threshold on that end of the spectrum as well to take full advantage of the better gas and obviously make more power. They have a learning curve so to speak.
Acura Integra's and RSX's do neither of these oddball scenario's though so running 94 octane in a bolt-on LS or base RSX will accomplish the task of emptying you bank account quicker and that is about it.
When crude oil is refined into gasoline, there isn't that much control over what comes out. Refining it separates impurities etc. in order of density. The heavy stuff is near the bottom, while the light stuff, like butane, stays near the top. The specific crude oil being used determines the amount of each blend available for mixing. Generally, if you just dump all the blend stocks together, you would end up with something around 88 octane. If you're selective and only mix the better, more detonation resistant on top, you can make 95 octane. But once you take out the good stuff, you're left with crap-something like 85 octane. Then you have to leave enough good stuff in the bucket to bring this weak rating back up to at least 87 octane. This limits the amount of high octane gas you can make but does not necessarily increase the impurities and contaminants. So lower octane fuel is not really dirtier, just less detonation resistant
All the truck and SUV driving people in middle America burn enough 87 crap to allow us to get 93 and 94 octane. All the Mercedes wheeling executives on the west coast burn up so much premium gasoline that 91 has become the standard there because you have to leave enough good stuff behind to make atleast 87 octane. West coast business success screws ya'll into only having 91 while I regularly fill up with 94