Here are a few of the all time greats and some of the movies they are most well known for, in bold are the ones I've seen and really enjoyed, I've seen Titanic and whilst it's great wasn't the biggest of fans and felt it was highly overrated:
Steven Spielberg- Indiana Jones, Schindler's List, Jaws, ET
Akira Kurosawa- Yojimbo, The Seven Samurai
The Coen Brothers- No Country for Old Men, Fargo, The Big Lebowski, Miller's Crossing, Burn After Reading
David Fincher- Fight Club, Zodiac, Curious Case of Benjamin Button, Se7en
Francis Ford Copolla- Apocalypse Now, The Godfather, The Godfather Pt 2
Alfred Hitchcock- North By Northwest, Vertigo, Psycho, Rear Window
Stanley Kuberick- Dr. Strangelove or: How I Learned to Stop Worrying and Love the Bomb, 2001: A Space Odyssey, Paths of Glory, Spartacus, A Clockwork Orange
Martin Scorscese- Raging Bull, Taxi Driver, The Departed
Clint Eastwood- Unforgiven, Million Dollar Baby, Gran Torino, Letters From Iwo Jima, Mystic River
Billy Wilder- Double Indeminty, Some Like it Hot, Sunset Blvd, Witness for the Prosecution
James Cameroon- The Titanic, The Terminator, Aliens, T2
Tim Burton- Batman, Sweeney Todd, Edward Scissorhands
That Tarantino Guy- All his movies
I know they are not all time greats but guys I really enjoy:
Guy Ritchie- Lock Stock and Two Smoking Barells, Snatch, Rock n Rolla
Darren Aronofsky- Pi, Requiem for a Dream, The Wrestler
Danny Boyle- Shallow Grave, Trainspotting, Slumdog Millionaire
Can't fault your list. I would add the following just for action:
Luc Besson - La Famme Nikita, Leon - The Proffesional, Angel - A, The
Fifth Element, The Messenger, The Lady
Takeshi Kitano - Sonatine, Boiling Point, Violent Cop, Fireworks, Brother,
The Blind Swordsman - Zatoichi
Takeshi Miike - 13 Assassins, Hara Kiri, Graveyard Of Honor, Dead Or Alive
Trilogy, Fudoh: The Next Generation
John Woo - Killer, Hard Boiled, A Better Tomorrow,
Hard Target, Face/Off, Red Cliff, Mission Impossible II