1. Season 27
The concept: Season 27 would have aired in 1990 (yes, the last episodes of Doctor Who aired at the same time as the first episodes of Red Dwarf and TNG), and would likely have seen the departure of Ace, heading to Gallifrey to become a Time Lord (yes, really), and the introduction of a new companion, Raine Creevy. The season possibly would have ended with the departure of Sylvester McCoy and the introduction of the 8th Doctor, played, at least in theory, by Richard Griffiths, best known for his role as Victor Dursley in the Harry Potter movies. We may have also seen the finale of the Cartmel Masterplan, which was an ongoing effort to restore a sense of mystery, and occasional menace, to the Doctor and the Time Lords.
How far along: It varied. There may have not been scripts, but there were at least story ideas and titles, such as Lungbarrow, Earth Aid, Thin Ice and Crime of the Century.
Why it was never made: Well, generally once a show has been cancelled, very few further scripts are put into production. The cancelation occurred after the final episode had been shot, and before it was broadcast, so really, after the last episode had been shown, all production stopped.
Why its on the list: Because seeing a resolution to the Cartmel Masterplan would have been nice. It was apparently resolved in book form in the now out-of-print, insanely-expensive novel version of Lungbarrow, but never on TV. Plus it would have been nice to have Ace get her own send-off, and to see the new companion. It really would have been interesting to see Richard Griffiths play the Doctor, as well.
The eventual fate: Earth Aid, Thin Ice and Crime of the Century, along with another story, Animal, were all released in audio form by Big Finish, with Sylvester McCoy as the Doctor, Sophie Aldred as Ace, Beth Chalmers as Raine and Angela Bruce as Brigadier Bambera. And they were good. Ace commanding a starship and doing her best Picard impression is a beauty to behold.