I think 2005's The New World was reasonably accurate, and oftentimes beautiful, though I guess the definitive take on that story has to remain Disney's Pocahontas, because the talking raccoon was left out by Terrence Malick.
To bookend Chinese imperial history, 1998's The Emperor and the Assassin seems to faithfully take on the known history of Ying Zheng's life, he being more or less the first ruler of a unified China, and Bertolucci's The Last Emperor, from 1987 did not take any egregious detours from fact concerning the pathetic fate of China's last imperial ruler. (It also featured Peter O'Toole, who seems to be working himself into half the movies I mention here lately...)
Meeko didn't talk... :(