I just started thinking of this just now:
Woody Allen-Highly prolific director whose films center around neurotic brand of humor although he's occasionally experimented
Robert Altman-Specialized in ensemble pieces and genre deconstruction. Played around with story conventions.
Wes Anderson-Characters are usually damaged from past relationships (usually family relationships), rich multisourced visual texture and score
Tim Burton-Specializes in animation or films with a strong emphasis on visual tone. Visual tone is Gothic in nature.
Mel Brooks-Low-brow film parodies
Joel and Ethan Coen-The brothers specialize in dark humor, filmic references to other genres, free association humor, offbeat characters, and evoking a strong sense of place
Sophia Coppolla-Experimental director with a strong feminist perspective
Kevin Costner-Drawn towards epics with a medidative pace
Cameron Crowe-His works are either a celebration of rock music or of a rock-n-roll free-thinking lifestyle. Notable for dialogue
Frank Dabranot-A modern-day Frank Capra, telling uplifting stories with picturesque cinametography. The Mist was somewhat of a deviation from this
Roland Emmerich-Tries to capture large-scale doomsday-like scenarios through telling the individual stories of a cross-section of society
Clint Eastwood-Spans all genres equally, films center around realistic human characters, emotions, and consequences.
John Ford-Specialized in Westerns and pieces set in his home country of Ireland. Although he evolved, his work was generally reinforcing of the American dream
Terry Gilliam-Films generally explore mythology, strong emphasis on his evocative fantasical mise-en-scenes
Christopher Guest-Comedies in an improvizational style with usually the same stock of characters.
Howard Hawks-Crossed genre, but always had strong dialogue and strong male hero characters
Alfred Hitchkock-Specialized in the art of suspense. Could cater style to mysteries, literary adaptations, pure terror films, political thrillers, espionage stories, or black comedies.
Ron Howard-Produces solid middle-brow entertainment which isn't particularly bold or innovative but solid. Specializes in docudramas.
Lasse Hollstrom-Movies resemble flowery, baroque novels
John Huston-Adventurous stories shot in faroff places
Alejandro Inarritu Gonzalu-Uses intertwining stories (usually about 3) to say something profound about the human condition
Charlie Kaufman-Plays around with unconventional storylines
Elia Kazan-Specialized in classic literary adaptations. Socially conscious
Stanley Kramer-Socially-conscious films
Stanley Kubrick-Experimental filmmaker who reinvented each genre he dabbled without being particularly subversive of them
David Lean-Specialized in the epic. He was British and chronicled stories at the fringes of the British empire such as India, Southeast Asia and the Arabian Penninsula.
George Lucas-Films named Star Wars....no seriously, his body of work isn't particularly big, but there's obviously a focus on special effects and a clear interest in myths and drawing on cultural references.
Terrence Malick-Long surrealist mood pieces with emphasis on narration.
Sam Mendes-Works from the inside out: Creates a portrait of a world, then the characters who inhabit it, before moving to story
Anthony Minghellia-Epic-style literary adaptations, delicate novelized treatment of the subject matter
Vincente Minelli-Specializes in musical, stylized, subdued, and colorful tones in mise-en-scene
Mike Nicholls-Usually has good source material to work from, big on literary adaptations, certain comic tones in all of his work, favorite among actors
Sam Peckinpaugh-Bloody, gritty takes on the Western
Otto Premminger-Stark films shot in a noir style through different types of drama. Generally bleak stories commented on societal institutions
Rob Rodriguez-Work marked by creative approaches to action scenes, interest in visual experimentation.
Ridley Scott-Stylized big-budget movies. Equally at ease with sci-fi, historical epic or crime drama, but from the looks of A Good Year, he stumbles in character-centered personal stories.
Kevin Smith-Low-bro self-referencing and pop-culture referencing comedies
Stephen Soderbergh-Often socially conscious and highly experimental in everything from narrational point-of-view to film stock. Considered independent in style
Stephen Spielberg-Although he has made a few historical epics of consequence (Color Purple, Munich, Schindler's List, Saving Private Ryan), he specializes in blockbusters. Strengths are special effects and storytelling.
Barry Sonnenfeld-Stories with fantasical and imaginative concepts.
Quentin Tarantino-Films influenced by Asian martial arts film but are fused with other elements. Usually a heavy amount of stylized violence is in films.
Lars von Trier-Beleives in stripping down moviemaking of its artificial elements. Also, he is somewhat anti-American.
Peter Weir-Delicate and meditative film style. Good track record of stretching actors past their comfort zones.
Billy Wilder-Could alternate genres but specialized in film noir and subversive comedies with great ability to write dialogue
Rob Zemeckis-Veers toward adventurous and fun stories. Liked to combine different elements technologically and stylistically (An animated rabbit and a mobster story, 3D special effects with mythology, a retarded man with inserted footage of elements in history). Bold visionary.
Ed Zwick-Sophistocated action stories