Car continues to run after the key is turned off?

I have a 1996 Honda Accord. I don't know why it keeps running after I turn it off. For 5- 10 seconds. It's starting to worry me. Any one have an idea what is happening?

Added (1). And is it safe to drive? I'm going on a trip and need to know.

KY is right about the dieseling, not much else I agree with though. Seafoam cure in a can seldom work. It is carbon buildup in the cylinder igniting the fuel and the fact that your carburetor will keep adding fuel because the engine is still pulling in air. On some models there were small solenoid that were wired to hold the idle up to its set RPM and when you turned off the ignition it would drop the butterfly's in the carb totally closed cutting off the air supply. You may want to look to see if your has one and it is working like it should. The other answer is to run the car flat out for about twenty seconds from a dead stop. You will no doubt see a trail of black looking smoke shooting out the exhaust, that would be the carbon. You only need to do this as needed and it may not be that often.

This is called dieseling and is very rare in modern fuel injected, computer controlled, cars of today. Dieseling is not nearly as common as it once was, because it most commonly occurs in engines equipped with carburetors. Built-up carbon in the ignition chamber can glow red after the engine is off, providing a mechanism for igniting unburnt fuel. Such a thing can happen when the engine runs very rich, depositing unspent fuel and particles on the pistons and valves. Similarly, rough metal regions within the piston chamber can cause this same problem, since they can glow red. It has also been suggested that an improperly rated spark plug can retain heat and cause the same problem. Hot vaporized oil gases from the engine crankcase can provide ample fuel for dieseling. An engine that runs too hot or too lean or is out of time may produce an environment conducive to allowing unspent fuel to burn. Your car is 18 years old so I would suspect you have carbon buildup. Purchase a can of Seafoam Motor Treatment and follow the directions to remove the carbon deposits in your engine. Click the link to see how this is accomplished with Seafoam. http://seafoamsales.com/vacuum-line-method-with-sea-foam/

When this happens the engine may even run backwards for couple seconds. Looks like your in good hands with some good advice.