I've seen some East Coast and CrossCountry services running close to four hours late due to various problems such as overhead wire problems, signalling problems and broken down trains.
In terms of my own delays I was once stranded in the south of France due to SNCF going on strike. I was due to get a TGV to Paris but only one that day was running. It would have been too expensive to find a hotel in Paris so we stayed in Nice and got the only train running to Paris the next morning (which, understandably, was rammed). We then got a Eurostar back to London and then a train back to Cardiff. We were over a day late but luckily our hotel was covered by insurance!
In terms of delays here, on 17th December I was delayed by over two hours on a 150/1 at Filton Abbey Wood. The irritating thing was that I could have got off at Patchway had I known there were delays, and even more frustrating, the service half an hour earlier was on time, but mine arrived two hours late. I could even see Filton Abbey Wood from where we were sat. To say I was angry was an understatement!