Fascinating thread. Really interesting to read what people put so much effort into to build up a collection of.
Leaving aside all collections that can be purchased in shops, as there's far too many for me to list, there have only ever really been two shows I've put the effort in to try and build up a complete collection of.
The first being The Bill - It was fairly late on in the show's run when I started collecting these, around the summer of 2006, but thanks to the likes of Gold, Alibi, Watch and Drama, I managed to build up a substantial collection of the later years. By the time the programme finished though, it was pretty obvious that nobody was going to rewind and do a complete run of the show from the start again so I'd pretty much lost hope by that point. Thanks to the DVD sets though, I've now managed to replace the versions I'd recorded with the sets purchased online and complete the collection. Luckily, I also had the four episodes not available on the DVD sets from my own personal recordings so finally have a full collection!
Second, and on a bigger scale, is Coronation Street - I currently have every episode of the programme from 5th April 1976 right through to the present day - bar one episode from 2002! All now on DVD. It occurred to me when finding this thread that in exactly a month's time it will be exactly forty years worth of episodes

(bar the one of course!).
I like the simplicity of collecting the long running programmes though. It becomes a habit due to the routine of the schedules and I like the idea of being able to dip into a point in the past and go back. With ongoing serials as well, you're never really in danger of wondering what to move onto when you complete the collection as the show just keeps on going.