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Disney

Before 1937, animation was really used in short films and parts of live action movies. Snow White and the Seven Dwarves is the first feature length movie, produced by Walt Disney Productions, it began development in 1934. Disney carried on with production with no support from family or anyone in the film industry, he mortgaged his home to help finance the film. Inspiration for the movie came from th ebook by the brothers Grimm (with multiple changes), though many scenes were based on German movies like The Cabinet of Dr. Calagari and Nosferatu. Jeckyl and Hyde provided the basis of the Witch's transformation. Disney used live actors as subjects which the characters were based on to make them realistic in shape.
The animation was well recieved, Disney won 11 academy awards and one full scale one. The money earned from the film was used to fund the animation studio where it was made and within two years, production had started on Bambi, Fantasia, Pinocchio, Dumbo, Alice in Wonderland and Peter Pan, as well as the Disney shorts which featured Mickey Mouse.

Tom & Jerry

The Tom & Jerry cartoons started in 1940 , they were created by Hanna-Barbera and produced by Fred Quimby. Over the 40s Tom's design became less detailed and the character became more humanoid in appearance (much like Garfield would). The original Tom was called Jasper, Tom and Jerry was a phrase the producers decided to use as the title and the name stuck. The cartoons went through multiple producers up until the 60s when Chuck Jones produces, many people dispute the differences made with  each different producer's run but I disagree -particularly with Jones' contemporary take on the duo, which adds a very 60s feel and is reminiscent of the Grinch (which Jones animated).

Warner Bros. Cartoons

Harman-Ising Productions created the original Loony Tunes, they also created Merry Melodies- similar to Disney's cartoons of the time, though not as successful. The character Bosko was popular among audiences.

Leon Schlesinger Productions developed the Loony Tunes animations and created some of it's best known characters, Daffy Duck, Elma Fudd, Bugs Bunny, etc. 

Warner Bros. bought out the company and continued to produce Loony Tunes. There were several companies under Warner Bros. label, Chuck Jones' company, which created the new Tom and Jerry cartoons and How the Grinch Stole Christmas. Hanna-Barbera Productions, creators of Scooby-Doo, Yogi Bear, the Flintstones, etc.