Of all the generations of Civic, the seventh-generation car is probably least known for its outgoing personality. That was a boon to sales when it was new; the seventh-generation's inoffensive nature and all-around versatility might have made it a bit generic, but generic is exactly what you need to sell a car to everyone. A decade later, though, these cars have hit the second-hand market, and it's time to install a bit of the soul that Honda purposely left out.
The seventh-gen's exhaust system is a bit more complicated than older cars', primarily because of the resonator. As pulsating sound waves travel through your exhaust system, they encounter a small chamber, called a resonator, which bounces them back onto themselves. This resonator contains pipes tuned to an exact length to capture and reflect wavelengths generally considered annoying and obnoxious. When those wavelengths bounce back, they cancel out on incoming wavelengths of the same range, eliminating the tone. The muffler at the end of the pipe only really serves to give a net reduction in sound energy; the resonator does the real work in terms of sound control.
Loud, Very Loud
If your definition of "improving" the car's sound characteristics involves making it ear-shatteringly loud, then there's a fairly simple approach for that. Simply removing the muffler, even cutting it off completely, will do very little in terms of altering the car's sound or making it louder. The resonator located under the car is the main component of the system. If you want to set off car alarms, the thing to do is to cut off the exhaust pipe before the resonator, weld in a straight section of tubing and install a straight-through, "fart can" muffler, like a RACtive Fireball, on the end of the system. This is fairly easy, given the system's layout, and it will definitely make sure everyone for two miles knows when you downshift.
The most sure-fire approach to achieving a reasonable exhaust note is to look into a full cat-back exhaust. There's a chance you could pick up some horsepower, and the better systems already had some engineering go into the sizing, material, and resonator or muffler matching. And it is important to match the muffler and resonator; you don't want one doubling up and killing sound waves that you want when the other already let them through. Aftermarket cat-back systems will often do without a resonator altogether, as most manufacturers prefer to combine the two functions in a single muffler. If you're going with a cat-back, then the best policy is to pony up and buy name-brand like Bassani, Mugen or Borla.
Piece by Piece
You can engineer your own system, provided that you follow a few basic rules. The first is not to go for the largest diameter, thinnest or lightest tubing available. When paired with an engine like the Civic's, this kind of tubing will vibrate in harmonic sympathy with the engine at certain rpm levels, inducing the dreaded and mind-numbing drone. Larger-diameter tubing will allow more high-frequency and potentially annoying waves to escape, and partially nullify the effect of a resonator or tuned muffler. So, pay special attention to your muffler selection if you're going with big tubes, and stay away from straight-through designs. If you do encounter drone, you can largely eliminate it by wrapping your entire cat-back section with adhesive header wrap, which will lower the tubes' resonant frequency and keep them from vibrating.