Do Some Lines
If you don't get by now that the best way to improve engine response is to make sure that the engine is getting plenty of fuel, then reading the rest of this probably won't help you. But, if you're cool with the whole "engine needs fuel" concept, there's someplace else you should look for problems with your engine response: your fuel lines.
The fuel pump sends fuel from the gas tank to the engine, but that fuel has to get there somehow. That's where the fuel lines come in. A leak or a kink in your fuel lines, even a tiny one, can rob your engine of performance. Because the fuel lines won't be able to maintain the pressure needed to transport the fuel through the lines, a car with a leaky fuel line won't respond quickly to driver inputs. The fuel lines are like train tracks: If there's a problem with the tracks, the train won't be coming through -- at least not a full speed.
If you have a big leak in your fuel lines, you'll probably know it because there'll be a puddle of fuel under your car when it's parked. A smaller leak or a kink in a line will be harder to detect, however. You visually inspect the lines or check fuel pressure using a...wait for it...fuel pressure gauge. That sort of test can be a bit much for people who aren't dedicated mechanics, and messing with fuel lines raises some safety issues. If you're not completely sure you can safely do the fuel pressure test and fix any problems you find, you're next step should be pulling out the yellow pages and finding a good mechanic.