These lists are always hard because I will invariably leave a film or filmmaker off the list. So understand that the films I list are only a drop in the bucket.
Cinematography:
For color, watch THE RED SHOES (1948) - Director of Photography - Jack Cardiff.
Cardiff was a master of the Three-Strip Technicolor process. The rich and colorful images he composes are the stuff dreams are made of. In fact, watch EVERY film Cardiff shot, especially for the team of Michael Powell and Emerich Pressberger (directors of THE RED SHOES as well as other masterpieces like BLACK NARCISSUS and A MATTER OF LIFE AND DEATH). Hell, he even made RAMBO: FIRST BLOOD PART II look fantastic!

For Black and White - IN COLD BLOOD (1967) - Director of Photography - Conrad Hall.
Hall is another D.P. whose work you should watch (ELECTRA GLIDE IN BLUE, FAT CITY, and AMERICAN BEAUTY are standouts) . He was from the new school of cinematography that knew how to manipulate the lighter cameras and faster film stocks by using light sparingly. The rich black and white photography of this picture is extraordinary, especially a scene toward the end of the film where the reflection of rain running down a pane of glass resembles tears running down the face of actor Robert Blake.

For camera movement and freedom - THE CROWD (1928) - Director of Photography - Henry Sharp.
Made just prior to the advent of motion picture sound, this extraordinary film by King Vidor attempted to break all the rules. The images were both realistic and expressionistic and with no burdensome sound equipment to tie him down, Sharp was able to move his camera about freely - strapping it to the back of a speeding car, sliding down a funhouse slide, or just tracking behind a character. It's a cinematic landmark.

DIRECTING:

THE SEARCHERS (1956) - John Ford
Ford is a master visual storyteller. He came from silent films so he knows how to tell his story in pictures, an artform that is being lost in filmmaking. He also knew how to photographs majestic landscapes as well as characters faces.

SEVEN SAMURAI (1954) - Akira Kurosawa.
Kurosawa is a master at EVERYTHING! Watch everything the man ever made. Study his shot compositions, his pacing, his editing, his blocking of actors, and you will be a great filmmaker.

JAWS (1975) - Steven Spielberg.
One of the greatest Horror/Thrillers ever committed to celluloid. Spielberg is brilliant at staging lengthy scenes without cuts, unbeknownst to the audience because the staging and the performances are so damn riveting. Also, his use of keeping the camera at water-level, in order to simulate something lurking beneath the surface, ratchets up the suspense even more.

STORY

THE SPANISH PRISONER (1997) - David Mamet.
Mamet is one of the great playwrites of past 40 years and his screenplays are just as brilliant. He loves the art of the con (many of his best works revolve around someone being played), and this brilliantly structured thriller boils down the elements of a great thriller in the vein of Hitchcock (complete with a Hitchcockian "MacGuffin" and the innocent man on the run) to its bare essentials. Plus, the dialogue is almost like music, almost a Blank Verse style of sentence structure.

SWEET SMELL OF SUCCESS (1957) - Ernest Lehman and Clifford Odets.
More dialogue that is extraordinary - both beautiful and sinister. You can't go wrong with dialogue such as, "I'd hate to take a bite out of you, Sidney. You're a cookie filled with arsenic". "Dallas, your mouth is as big as a basket and twice as empty!", and, "Watch me run a 50-yard dash with my legs cut off!"

SHOCK CORRIDOR (1963) - Samuel Fuller.
Sam Fuller was one of the greatest storytellers of the 20th century (read up on the man - his life is as incredible and fascinating as one of his many great yarns). This film about a newspaper reporter committing himself to an insane asylum in order to catch a killer is a masterpiece of subversion. It confronts the most high-profile social ills of the day (ills that still plague us 52 years after the picture's release), and shoves them right in the audiences faces. Basically, Fuller loved to rub our noses in our own shit... but still make a damn riveting picture.

THE RED SHOES (1948) - Passionate, extraordinary colors - Jack Cardiff (absolutely incredible cinematography)

RAIDERS OF THE LOST ARK (1981) - Greatest adventure picture - Harrison Ford

POINT BLANK (1967) - Tough, enigmatic, cool - Henry Berman (extraordinary editing job)

SUNRISE: A SONG OF TWO HUMANS (1927) - Beautiful, expressionistic, human - F.W. Murnau (his vision/direction is the stuff dreams are made of)

ANNIE HALL (1977) - Hilarious, romantic, neurotic - Woody Allen