First broadcast today in 1963 was The Firemaker - the fourth and final instalment of An Unearthly Child. The TARDIS arrived in a strange misty forest at the end - the first indication to viewers that this was going to be an on-going serial, comprising distinct stories. After the first episode, there hadn't been a lot of Science-Fiction in the series, but next week's episode threatened a radiation danger, and promised a dead planet...
The Invasion reached its seventh episode in 1968. This was the first time a story had exceeded six episodes since The Daleks' Master Plan in nearly 1966, and it still wasn't finished.
Then, in 1988, Season 25 arrived at its final story, with Part One of The Greatest Show In The Galaxy. The preceding Cyberman story had originally been earmarked to end the season, but episodes were moved about so that the silver anniversary story opened on the 23rd November itself. This led to a continuity error - Ace being seen to wear a badge in Silver Nemesis, which she doesn't actually obtain until this story.
Now that stories are out on DVD or Blu-ray, we can watch them in any order we want. There are those who question Jo Grant's incredulity about the TARDIS in Colony In Space, when she's seen it dematerialise in front of her eyes in The Claws of Axos. This has led them to watch these stories in reverse order.
Another switch around some fans prefer is to swap Inferno for The Ambassadors of Death. The Doctor sort of hands Liz over to Dr Cornish to assist him at the end - which is marginally more satisfying than her just vanishing after Inferno - returning to Cambridge off screen.
Where do you place K9 & Company, if watching stories in order? Technically it comes between Logopolis and Castrovalva - but as the latter follows on directly from the former, you really can't pause to watch Sarah Jane Smith and K9 muck about with Hecate-worshippers in deepest Mummerset mid regeneration. As all of Season 18 is linked together, I tend to watch it after Castrovalva, before moving on to Four to Doomsday.