Q:

Was I nearly involved in an accident?

This is a while ago but it has been bugging me now and then.
On September 11 2011 (yes exactly 10 years after 9/11!) I was flying Easyjet 3467 from London Stansted Airport (STN) to Copenhagen (CPH). Scheduled departure was 18:40 local time but the flight was heavily delayed (around 4 hours as I recall) due to another bizarre incident. 
Anyway, as we were finally sitting in the plane and taxiing, suddenly the pilot announces that he just got info that another airplane had been heading to land just where we were and had only been some 60 seconds away! A lot of passengers seemed to gasp for air and the pilot sounded quite shocked as well. But there was no other explanation added.
Is there a database of such events so I could look up more about what happened?
I found the flight on FlightStats (sign in required) but there were no real info.

A:

No, you were not nearly involved in an accident. 
If the flight crew is ready to go, an Airbus A320 takes about 40-50 seconds from the moment take-off clearance is given until lift-off. As soon as the aircraft is off the runway, the next one can land. On some busy airports, 60 seconds between take-off clearance and the next landing is a daily occurrence.
In 60 seconds, there is a lot that can prevent an accident. For example, ATC could instruct the incoming aircraft to go around should the departing traffic not be ready to take-off. This is quite a normal event which happens every day at busy airports around the world. In such a case, the aircraft ready for take-off would have to wait for the incoming traffic to pass overhead. It sounds like you may have experienced such an event. 
Here is a video of something similar happening in Birmingham.
Since it is a 'normal' event, there is no central database that tracks these issues. 

A:

The term you want to look for is not "accident", but "incident".

To figure out whether or not a situation qualifies as an “aircraft accident” we must look to the definitions in Part 830. The NTSB defines an “aircraft accident” to mean “an occurrence associated with the operation of an aircraft which takes place between the time any person boards the aircraft with the intention of flight and all such persons have disembarked, and in which any person suffers death or serious injury, or in which the aircraft receives substantial damage.” The first portion of this definition is especially important to note for maintenance and ramp personnel. The initial threshold for classification as an aircraft accident is that the aircraft is being operated “with the intention of flight.”

Since no injury or damage occurred, the even would be classified as an "incident".

In the US, NASA runs the Aviation Safety Reporting System, a publicly searchable database of accidents and incidents.  The data are mostly about events in the US, although some international incidents are included as well.  The incident you mentioned doesn't appear.
The European equivalent appears to be ECCAIRS.  Unfortunately, access to that database is "restricted to authorized authorities."

