I'd add Cary Grant and Katharine Hepburn in Bringing Up Baby, The Philadelphia Story, or indeed anything. I'd also add Harrison Ford and Kelly McGillis in Witness, Anthony Hopkins and Emma Thompson in The Remains of the Day, and Clark Gable and Vivien Leigh in Gone with the Wind (that's just off the top of my head). :)

Of course, a cousin to this article would be to discuss friendship films - Butch and Sundance (Butch Cassidy and the Sundance Kid), Thelma and Louise (Thelma & Louise), Red and Andy (The Shawshank Redemption), etc.