You can read all the actors who could've been Doctor's one through seven here, the list below completes the story starting with the Eighth Doctor.
(In all cases I've tried to avoid the names that were merely tabloid speculation and stuck to those who were either considered, approached or auditioned for the role.)
Richard Griffiths had already been considered for the role of the Fifth Doctor, and had Doctor Who not been cancelled in 1989 then chances are he would've been the Eighth. He was certainly the front runner in John Nathan-Turner's eyes, but alas, the Seventh Doctor and Ace walked off into the woods...
Just before Doctor Who left our screens, Paramount Pictures expressed interest in producing a US movie version. They had two people in mind for the role, one was Bill Cosby (!) and the other was Michael Jackson (!!!!!!). I can't even begin to imagine how Jackson would've played the Time Lord, actually I can - think of Johnny Depp as Willy Wonka, there you go! Even the BBC thought it was a bad idea, so let's all be thankful that it didn't happen.
In the early 90s, whilst the rights moved from studio to studio, a pre-Bond Pierce Brosnan was attached to a possible big screen version. Another option saw Rutger Hauer linked to a script titled Doctor Who: Last of the Time Lords - sounds familiar!
A flurry of comic actors were also considered for the role, including Eric Idle, Michael Palin, Billy Connolly, Tony Slattery, Rik Mayall, Jon Sessions and Rowan Atkinson (above). Atkinson was the only one of this bunch who screen tested, he would go on to play the Ninth Doctor in The Curse Of Fatal Death.
Ninth Doctor Christopher Eccleston was invited to audition for the role, but declined. As did the Twelve Doctor Peter Capaldi.
UPDATE Nov 17th 2014
Capaldi spoke about his decision to decline the audition at the launch event for the Doctor Who series 8 DVD release:
"I knew I wouldn’t get it. I loved the show so much that I didn’t want to have anything to do with it unless it was going to be me. I didn’t want to have the disappointment and go through all the palaver of jumping through hoops for something that I would never get. Because I knew it was an American pilot, and I knew they would go for somebody who was well-known - which Paul was, and he was fantastic. So I didn’t go along for the audition. I said to my agent 'Thank you very much, but I don’t want to go along'."
We're nowhere near done with Eighth Doctor contenders! Both Anthony Head and Tim McInnerny auditioned for the role. Head, best known as Giles from Buffy The Vampire Slayer, would appear 10 years later in the Tenth Doctor episode School Reunion, and McInnerny two years after that in The Planet Of The Ood. Other actors who screen-tested include Nathaniel Parker, Peter Woodhead and Mark McGann (above). I imagine that must've proved awkward when his big brother eventually won the role.
The man who was originally picked for the job by producer Philip Segal was the actor Liam Cunningham (above), you may know him from Game Of Thrones and he also appeared in the Matt Smith story, Cold War. Cunningham had the backing of the BBC too, but FOX had other ideas. They did not like Cunningham and insisted Segal screen test some new candidates.
This was when Paul McGann came to the producers attention, but once again FOX did not agree with the Philip Segal's choice and suggested he cast Harry Van Gorkum in the role. But when Eric Roberts was cast as the Master, FOX were happy to have an Oscar-nominated movie star on-board, so they approved the casting of McGann.
I know it says at the top "Actors who were considered for the Doctor" and I promised not to include tabloid speculation, but stick with me on this one.
In 2003, to celebrate the 40th Anniversary of the show, the BBC set about creating what would become The Scream Of The Shalka. It was recently revealed on a DVD extra that after the production team discovered he had an interest in the part, Robbie Williams was actively pursued to voice, what was at the time, the official Ninth Doctor! It's maybe not quite as crazy as Michael Jackson but it still beggars belief! Fortunately, Robbie's busy schedule prevented this from occurring.
More than anything, I think this really shows just what the BBC thought of Doctor Who at this time, and if it wasn't for the guiding hand of Russell T Davies then you have to wonder just what might have happened when it came to casting the official Ninth Doctor.
Russell T Davies originally offered the role of the Ninth Doctor to Hugh Grant. Grant is the third actor on this list who appeared in The Curse Of Fatal Death, where he briefly played the Twelfth Doctor. He turned Davies down because he thought the reboot series would likely be a "bit naff", but later expressed regret when he saw how well the show turned out.
With Hugh Grant out of the running, casting director Andy Pryor suggested a young theatrical actor by the name of David Tennant. He was considered too young for the part, I've no idea what happened to him !!! Producer Jane Tranter revealed that she considered casting Judi Dench as the Ninth Doctor, that would've been interesting. David Suchet's was also in consideration at one time.
The final round of auditions for the Ninth Doctor consisted of Christopher Eccleston, Bill Nighy (above) and Alan Davies. Nighy was offered the part, but it's unclear if he was actually offered the role of the Ninth Doctor or he was called upon when Eccleston decided to leave. It seems more likely that it was for the role of the Tenth Doctor as he has said his reason for declining the role was that he was no longer interested in the part. Nighy would appear in the Eleventh Doctor episode, Vincent And The Doctor.
Its worth pointing out that if Russell T Davies had stayed on as showrunner for the Eleventh Doctor's era he was considering casting a woman in the role, later revealing that Catherine Zeta-Jones would've been his ideal choice.
Steven Moffat revealed that he struggled to come up with a short list of older actors for the role of the Eleventh Doctor, so he ended up auditioning a lot of people in their 20s. One of those people was Mathew Horne. The Gavin & Stacy actor joked in an interview that after the decision was made the production team had rung up the wrong Matt!
Someone who is not in his 20s is Paterson Joseph. Although it's never been officially confirmed that he auditioned for the role of the Eleventh Doctor, it has often been implied. On his own Blog Neil Gaiman wrote "I know one black actor who was already offered the part of the Doctor, and who turned it down.". At another time Gaiman revealed "I was rather disappointed that Paterson Joseph didn't get it last time, although I've loved Matt." Paterson Joseph had appeared in the 2005 episode Bad Wolf.
Finishing off with the casting of the Twelfth Doctor. Steven Moffat revealed his list contained one name, Peter Capaldi, and maybe it did, but actor Ben Daniels had this to say: "I was approached and asked if it was something I'd be interested in doing....when I eventually managed to peel myself off the ceiling, I said, 'Yeah, of course it'd be something I'd be interested in doing. But I also knew from the outset that there was a name ahead of my own on that list that they were very interested in....about two weeks before that live reveal event - I was told that their shortlist had got much shorter! But it didn't mean I wouldn't come back into the frame." Clearly he didn't come back in to the frame, but it's interesting to read that the 'shortlist had got much shorter'.
I expect in years to come we will discover other actors who have been considered for the role of the Doctor, but for now that's the lot.
Source for Ben Daniels interview: Digital Spy