Frequency scanning does not mean all you do is listen to the police. You can also hear commercial jetliners and military aircraft (if your scanner can tune to those frequencies). Quite personally, I think listening to the commercial airliners is the most interesting part of scanning.
Across the United States, there are thousands of airports, both big and small. Each airport has its unique frequency. Finding out the frequencies for every airport would take forever, so I can not provide you with specific frequency information. But, I do know of some links where you can get most of the information you need. Check it out in my Links section.
To not leave you in the total dark, I do provide some information about the aviation frequency settings.
108.000-136.000 - The typical aviation frequencies. You can get these on "a little less than top-of-the-line" scanners. You can hear commercial airliners, small single-engine airplanes, some airports beacons (which only make an annoying hum), flight service stations, and most civilan control towers. (Spacing 0.025 MHz. AM mode)
225.000-406.000 - The military aviation frequencies. You can only get these on "top-of-the-line" scanners. You can hear military transport jets, F-16s, Navy Blue Angels, other airport beacons (which only give off an annoying hum, like said above), military bases with towers, and aircraft carriers. You can also hear some satellites within these frequencies. (Spacing 0.1 MHz. AM mode)
Learning how aviation frequencies work is tricky at the beginning. There are a lot of terms needed to be understood before any of it can make sense. Let me show you an example of an airport frequency make-up. This is a frequency example for Wittman Regional Airport in Oshkosh, Wisconsin.
OSHKOSH (WITTMAN REGIONAL)
ARTCC=Chicago Center           Sectional Chart=Green Bay, WI
OS NDB=395.000 KHz (356 degree heading, 6.6 nautical miles)
What this all means:
ARTCC: Chicago Center: ARTCC stands for "Air Route Traffic Control Centers." The United States Airspace is divided into twenty sectors, each usually surrounding a major city (such as Chicago). Aircraft are directed through the Center's airspace by air traffic controllers in the Center. It keeps the air traffic under control within and outside major airports. Wittman Field (Oshkosh, WI) is actually at the verge of Chicago Center's airspace. Seventeen miles north-northeast, over Appleton, WI, is airspace owned by Minneapolis Center.
Sectional Chart: Green Bay, WI: The United States, besides having sectors for ARTCC, has 37 sectors reserved for Sectional Aeronautical Charts. Flight Service Information is transmitted from here to airports in its sector (see FSS).
Main Tower: The control tower on the field. Unlike most airborne frequencies that you can hear hundreds of miles away, there is a limited range between your scanner and the tower. You usually will hear the tower directing the aircraft to land. Their frequencies are usually below 125 MHz.
Approach: This frequency usually comes from airborne aircraft. Generally, it means "the reserved airspace around the airport." This reserved airspace can be as far as fifty miles from the airport. If the aircraft preparing to land (or just passing through) wants to request a course adjustment, they call the tower who "owns" the airspace to see if any other aircraft are in the area.
Departure: This frequency usually comes from airborne aircraft that are leaving the airport. When traffic is heavy, air traffic controllers on the ground will use the frequency to direct the departing aircraft into safe airspace.
Ground: This frequency is used by air traffic that is on the ground. Ground control (usually transmitted on 121.900) directs pilots safely to the runway. It is usually used around major airports with large numbers of ground traffic, but occasionally smaller airports use it during busy times.
Unicom: This is a frequency usually used by small aircraft. With this system, the pilots of the aircraft determine when and how they want to land or take off. Usually, the pilot announces over the frequency his intentions to alert other aircraft that he is in the area. Unicom also allows pilots to communicate to the base operator on the ground to request information on fuel prices and other important needs. (see General Aviation Frequencies)
FSS: This stands for "Flight Service Station." Flight service stations provide pilots with important weather information and regional altimeter settings. The frequencies for each individual flight service station can be found on the sectional charts.
ATIS: ATIS stands for "Automatic Terminal Information Service." It is recorded information on active runways, weather conditions, and other warnings to alert pilots in advance. It is usually used around major air terminals. They can be found also on the sectional charts.
OSHKOSH VORTAC and OS NDB: VOR or VORTAC are VHF Navigation Stations, usually sitting betweeen 108 and 118 MHz. These beacons usually make a tone (like I specified above), although some have voices that tell of current weather conditions. Pilots use their radio navigation systems to follow that beacon to the airport. However, like the second beacon for Wittman Field, some beacons give a course direction and distance information to the airport. When pilots reach the beacon, they follow the given instructions until they reach the airport site.