Me too and I remember it like it was yesterday. I'm not sure if the missle was an errant launch by the navy who was active in the area that night (highly unlikelu IMO) or if it was a deliberate terrorist attack (I'd bet the ranch) but I know that immediately following the crash people were coming forward...within an hour of the crash...claiming to have seen a light streak from the surface to the plane just before the plane exploded.
In First Strike: TWA Flight 800 and the Attack on America James Sanders and Jack Cashill make a pretty convincing case that the Navy was trying to shoot down an explosives-laden small aircraft that was trying to collide intentionally with TWA 800. I know the theory sounds far fetched, but their argument is a plausible explanation of a lot of facts that don't fit together any other way.
IF TWA Flight 800 was brought down by a surface-to-air missile, it is highly unlikely that it was an act of terrorism.
There are two facts that weigh very heavily against a terrorist attack with a missile:
1. A terrorist who wanted to shoot down a passenger jet flying out of JFK Airport in New York City would not have positioned himself so far east of the airport, where an eastbound trans-Atlantic flight would have been at a very high altitude.
2. Flight 800 was actually flying through the area that evening at a somewhat lower altitude than normal. It had been instructed to reduce its altitude by several thousand feet in order to clear a flight path for a northbound flight to Providence, Rhode Island that was running behind schedule that night. A terrorist looking to shoot down a passenger jet could not have foreseen this when positioning himself to carry out the attack.
Interestingly, Item #2 is one of the things that lends some credence to the theory of an accidental shoot-down during a military exercise.