I Interviewed recently with a 767 cargo operator for a Captain position abroad and I had an accident back in 92 that caused me to ditch a 172 in the Bahamas due to an oil pump failure. This particular employment did have this "No history of accidents or incidents" note in the application form but I thought I gave it a world anyway. Sure enough, during the interview they wanted me to tell them about the accident and what have I learned from it, What would you have done differently, that sort of thing. After the interview was almost over, they produced an NTSB report of the accident and asked me if this was the accident in question, I confirmed that it was and we concluded the interview. Later on that night the position was offered to me.
An accident in your record is NOT a career killer but the circumstances around it and the recency of the event play a part though. If it was a mechanical like in my case, I don't thing that it will have any effect. But if it was something that you caused or helped to cause, still not a career killer but the more time that has elapsed since the accident the better because your event free history since then would be a good indicator that you have grown and matured as a pilot.
If it is something recent that is still under investigation, I recommend to stay put at your current gig until its resolution.
And most important of all, DON'T LIE IN THE APPLICATION. Before you show up at the interview they do their homework. They might forgive you having made a mistake when you where younger in your career, they will not forgive you being deceitful.