Tought I'd try a new response format. Rather than trying to pick one or making a top 10 list (both extremely hard if not impossible), I will select my favorite film and the two runner ups of each film genre. Unliked SnakeDoctor, I do lump a series together as one if and only if i likethe sequels. I note my favorite installment of a series in parenthesis. These genres and descriptions are from Wikipedia.
Action story in which the protagonist usually takes a risky turn, which leads to desperate situations (including explosions, fight scenes, daring escapes, etc.).
Favorite - Nolan's Batman Series (BB)
Runner-Ups - Inception, Casino Royale
Adventure story about a protagonist who journeys to epic or distant places to accomplish something.
Favorite - Indiana Jones Series (RotLA)
Runner-Ups - The Mummy ('99), Pirates of the Caribbean: Curse of the Black Pearl
Animation use of computer renderings or drawings (or occasionally photos of representational objects, known as stop-motion animation or claymation) shown in a sequence in order to depict an action or event rather than using the filming of live actors.
Favorite - The Lion King
Runner-Ups - Toy Story Trilogy (TS3), Tangled
Comedy story that tells about a series of funny or comical events, intended to make the audience laugh.
Favorite - Dumb and Dumber
Runner-Ups - Anchorman, Robin Hood: Men in Tights
Crime story about a crime that is being committed or was committed. It can also be an account of a criminal's life
Favorite - Leon: The Professional
Runner-Ups - City of God, Good Fellas
Drama depends mostly on in-depth development of realistic characters dealing with emotional themes. Dramatic themes such as alcoholism, drug addiction, infidelity, moral dilemmas, racial prejudice, religious intolerance, poverty, class divisions, violence against women and corruption put the characters in conflict with themselves, others, society and even natural phenomena.
Favorite - Adaptation
Runner-Ups - Matchstick Men, Eternal Sunshine of the Spotless Mind
Fantasy story about magic and supernatural forces, rather than technology, though it often is made to include elements of other genres, such as science fiction elements, for instance computers or DNA, if it happens to take place in a modern or future era.
Favorite - Star Wars Trilogy (ESB)
Runner-Ups - The Lord of the Rings Trilogy (FotR), The Chronicles of Narnia Series (TLWatW)
Historical story about a real person, event or time period.
Favorite - Gladiator
Runner-Ups - Catch Me If You Can, Lord of War
Horror story that is told to deliberately scare or frighten the audience, through suspense, violence or shock.
Don't like horrors
Musical story in which songs sung by the characters are interwoven into the narrative, sometimes accompanied by dancing.
Don't like non-animated musicals
Science Fiction Similar to fantasy, except stories in this genre use scientific understanding to explain the universe that it takes place in. It generally includes or is centered on the presumed effects or ramifications of computers or machines; travel through space, time or alternate universes; alien life-forms; genetic engineering; or other such things.
Favorite - Planet of the Apes (original)
Runner-Ups - Jurassic Park, The Matrix
War concerned with warfare, usually about naval, air or land battles, sometimes focusing instead on prisoners of war, covert operations, military training or other related subjects. At times war films focus on daily military or civilian life in wartime without depicting battles.
Favorite - Saving Private Ryan
Runner-Ups - The Last Samurai, Band of Brothers
Western devoted to telling stories set primarily in the latter half of the 19th century in the American Old West
Don't like westerns
