-Dominic West
Which character: Mance Rayder
Why did he say no: He didn't want to stay away from his family for 6 months
-Izzy Meikle-Small
Which character: Sansa Stark
Why she's happy that she didn't get the part: "I was a bit sad, because the show’s massive, but I’m not that unhappy, because they all show a lot of flesh, don’t they? I don’t think my parents would be happy."
-Sam Heughan
Which character: Renly Baratheon and Loras Tyrell
According to interview with Vulture, he auditioned for 7 times but lost it because everyone was going in for those parts.
-Sam Claflin
Which character: Jon Snow, Viserys Targaryen
Why did he say no: Because of his commitment to Pirates Of The Caribbean: On Stranger Tides
-Gillian Anderson
Which character: unknown
"My 18-year-old cannot believe that I would turn down Game Of Thrones or Downton [Abbey] — things she loves to watch."
Source.
Excuse to discuss actors who almost got the part in films/tv shows.