I like A Perfect Murder (1998), which is a remake of Hitchcock's Dial M for Murder (1954) because it isn't a strict remake... They change a few things and put it in a, then, contemporary setting... The original is still better, but I like having both of them...
My favourite has to be Vanilla Sky (2001) by Cameron Crowe.. It's a remake of a Spanish film Abre Los Ojos (1997) (Open Your Eyes) by Alejandro Amenábar... Crowe's movie captures some of the spirit and mood of the Spanish original despite feeling very American and starring Tom Cruise... Interestingly, Penelope Cruz plays the same role in both films... Both great movies that owe a lot to Hitchcock's Vertigo
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