I've watched Hidalgo, Spirit, The Black Stallion (VHS), the Seabiscuit documentary, Flicka (the new one), Black Beauty, Dreamer, and Secretariat.
I really enjoyed Spirit, Hidalgo, and Secretariat.
I know you mentioned movies only but I've also read the book Seabiscuit, My Friend Flicka, Dreamer, Brumby the Wild White Stallion, the Thoroughbred Series, War Horse, the Misty of Chincoteague series, and Black Beauty just to name a few of the bigger ones.
I feel that a lot of the times the books are better than the movies. More detailed, leaves a lot more to the imagination.