These Rachel Portman scores:

Emma, Legend of Bagger Vance, The Cider House Rules, Oliver Twist.

John Barry:

Out of Africa, Dances with Wolves, Somewhere in Time, James Bond Themes/Music,

Ennio Morricone:

The Mission, Cinema Paradiso, The Good, the Bad and the Ugly, The Untouchables, Once upon a time in America, Once upon a time in the West

John Williams:

E.T., Jurassic Park, Amistad, Indiana Jones, Empire of the Sun, Selections from Schindler's List and Saving Private Ryan, Selections from the Star Wars Saga Films (Yes even the new ones), Superman, The Patriot, Far and Away, Always, Close Encounters of the Third Kind.

Jerry Goldsmith
The Edge, First Knight, Air Force One, The Ghost and the Darkness, Rudy, Total Recall, Star Trek (multiples), Poltergeist, Gremlins, The Secret of Nimh, First Blood, Alien, Chinatown

Randy Edelman
Last of the Mohicans, Dragon: The Bruce Lee Story, Dragonheart

Hans Zimmer
Inception, Batman series, Kung Fu Panda, Pirates of the Caribbean, The Pacific, Sherlock Holmes, Angels & Demons, DaVinci Code, King Arthur, The Last Samurai, Spirit: Stallion of the Cimmarron, Black Hawk Down, Pearl Harbor, Gladiator, Mission Impossible, The Prince of Egypt, The Thin Red Line, The Rock, Broken Arrow, Crimson Tide, The Lion King, A League of their Own, Backdraft, Radio Flyer, Driving Miss Daisy,

Brian Tyler:
The Greatest Game Ever Played, Annapolis, Children of Dune

James Horner:
Braveheart, Titanic, Star Trek II, Something Wicket This Way Comes, Cocoon, Aliens, An American Tail and American Tail 2, Willow, Batteries Not Included, The Land Before Time, Field of Dreams, Glory, The Rocketeer, Patriot Games, Sneakers, Legends of the Fall, Apollo 13, Jumanji, Spitfire Grill, Deep Impact, Mask of Zorro, Enemy at the Gates, A Beautiful Mind, The Missing, Troy, The New World, The Boy in the Stripped Pajamas.

Alan Silvestri:
Forrest Gump, The Polar Express, Cast Away, Contact, Father of the Bride, Back to the Future, The Abyss, Predator, Flight of the Navigator, Who framed Roger Rabbit, Romancing the Stone (80's Yeah!).

Randy Newman
Ragtime, The Natural, Parenthood, Maverick, Toy Story, James and the Giant Peach, Michael, Pleasantville, A Bug's Life, Cars,

Thomas Newman
Fried Green Tomatoes, The Shawshank Redemption, Little Women, How to make an American Quilt, Phenomenon, The Horse Whisperer, Meet Joe Black, American Beauty, The Green Mile, Pay it Forward, Road to Perdition, Finding Nemo, Angels in America, Cinderella Man, Wall-E, Skyfall

Maurice Jarre:
Ghost, Dead Poets Society, Witness

Elmer Bernstein
Ten Commandments and others.

Henry Mancini
The Pink Panther theme and others.

Random less knowns:
Truman Show, The Piano, The Man from Snowy River, Half Light, Morrowind Soundtrack, To Kill a Mockingbird, Never Ending Story, Tron Legacy, Chariots of Fire and Bladerunner. EDIT: Forgot Tuck Everlasting.

There are a ton more and I'm not doing justice to a comprehensive list, but it's a start.