I've had three experiences of an overshoot.
First one was at Newcastle Central, one of the East Coast drivers managed to overshoot platform 4 by two carriages. People still tried to open the doors though even though there was no platform. As it was then blocking a train from Platform 3 which was departing first we were told to go across the bridges to go back into the station. Arrived 14 minutes late after crossing back over the bridges.
Second time, on a certain Southern TOC (not actually Southern) the driver misjudged the braking distance, and all the passengers could hear was 'Clunk'. The driver had managed to couple up to the unit that was already occupying part of the platform, thankfully that seemed to stop us because as soon as we heard the 'clunk' of the trains connecting we came to a sudden stop. The driver apoligised, saying 'Sorry about that, some people think it's funny to just park a train in the middle of a platform.' The train in front was about 1 coach away from the buffers, and thankfully for the driver everyone had a laugh about it, one person said 'Trains bang on time for a change, although I don't want to go through that every morning just for my train to be on time.'
Third time was on the T&W Metro, the driver managed to miss two stations. They missed Gateshead, and then Monument. Monument was a slight over run but Gateshead we had no chance of stopping in time, in fact by the time we would have stopped we probably would have only had the rear two doors of the train on the platform. At Monument they managed to overshoot, but it was only the front set of doors and the driver got out and isolated them just for that stop. They still work for Metro though (4 years on).
I have missed Hebburn on the Metro, but that was due to some 'uneducated youths' spreading leaves across the tracks, obviously they knew it caused serious wheelslip and we ended up just missing the station altogether. I do believe the station was then closed at police request. Driver couldn't be blamed for that one though.