Back when the European from Harwich to Scotland was diverted to run via the GEML, it stopped at Shenfield, then next at Watford Junction after going round the North London line. The Shenfield stop was around 0830 and of course to your average punter it looked very much like a Norwich-Liverpool Street service. I observed several people dive across the platform onto it from my Southend Vic-Liverpool St on more than one occasion, thinking they would get a quicker run to London, and indeed on the one time I used it to visit my then Girlfriend in Milton Keynes someone did it then.
Visiting the same GF, I normally used the then (this is 1987) only intercity service to run via the Northampton loop. This was one of the pick up only services at Watford and on one occasion I caught this train when there were high winds and a 50mph speed restriction. Two young lads jumped on proclaiming they could just jump off at Watford, only the stop was cancelled to reduce the delay and they had a panicked ride to MK, although the guard was good with them he did explain they should not have been on the train to start with.
In the early 80s I was on a railtour with what is now the East Anglian Railway Museum at Chappel in Suffolk. They had hired a Class 105 DMU to go to Didcot Railway Centre, via a thrash up the MML, then Bedford - Bletchley - Oxford - Didcot. All the seats were sold out but as we left Shenfield where my Dad and I picked the train up, two guys didn't have seats. Turns out, despite clear announcements (I remember them distinctly) and an odd looking train, to ladies decided it was the London train and had got on. After much fussing, they were eventually deposited at Cricklewood....
I've only slept past my home stop once, and it was just one stop. I woke as the train left my stop at Rayleigh, but thought I'd be OK as I should get to the next one just before the last train up was due. Except we were running about 5mins late and the last up was already pulling out as we arrived. There was no cab rank at Hockley then, but there was still a member of staff on duty back then and he took pity on me and got Rayleigh to send one.