Movie Dogs

Asta, in the various The Thin Man films.
Babe (movie) featured Border Collies.
Benji had several movies.
Pete the Pup (or "Petey"), a Pit Bull with a ring around one eye, in the Our Gang (later known as The Little Rascals) shorts produced by Hal Roach and later, MGM. A number of dogs played the role.
The film Cats & Dogs postulates an ongoing war dating back to ancient times between cats and dogs. The main character, a Beagle named Lou, is voiced by Tobey Maguire, later better known for portraying Spider-Man.
Devil Dog: The Hound of Hell, from the film of the same title
The many dog stars of Good Boy!, including the main character, Hubble, a Border Terrier, voiced by Matthew Broderick.
Rin Tin Tin, first dog star, a German Shepherd found in a trench by an American soldier, has appeared in films since 1922. All subsequent dogs in the part have been descendants of the original. Also on television.
Lady and the Tramp, from Walt Disney's movie of the same name.
Lassie Come Home (1943), starring Elizabeth Taylor and Roddy McDowall, many sequels and also a television show. Lassie is always played by a male collie.
Moses, the chalk outline dog in Dogville
Old Yeller (1957), a children's film, originally a novel by Fred Gipson
Otis, the Pug in The Adventures of Milo and Otis
Toto in The Wizard of Oz
Einstein and Copernicus in the Back to the Future Trilogy
Milo, Stanley Ipkiss' dog in The Mask
Frank, the alien dog in Men in Black
Hooch, the Dogue de Bordeaux costar of Turner and Hooch
the many dog stars of the mockumentary Best in Show
Fang, Hagrid's mastiff in the Harry Potter movies.
Fluffy, the three-headed dog in Harry Potter and the Philosopher's Stone
A transfigured Sirius Black in Harry Potter and the Prisoner of Azkaban
Verdell, The Brussels Griffon in As Good as it Gets
Blood, the talking dog in A Boy and his Dog