Despite being very energetic, determined and much larger, Tom is no match for Jerry's wits. Jerry also possesses surprising strength for his size, approximately the equivalent of Tom's, lifting items such as anvils with relative ease and withstanding considerable impacts.

The first Tom and Jerry short, Puss Gets the Boot, features a cat named Jasper and an unnamed mouse, named Jinx in pre-production. The basic premise was the one that would become familiar to audiences, described in The Art of Hanna-Barbera as "cat stalks and chases mouse in a frenzy of mayhem and slapstick violence." Though the studio executives were unimpressed, audiences loved the film and it was nominated for an Academy Award.

Barbera estimated the typical budget of $50,000 for each Tom and Jerry cartoon which made the duo take "time to get it right". A typical cartoon took around six weeks to make.

Mammy Two-Shoes is a heavy-set middle-aged African American woman who takes care of the house. Whether she is a housemaid or the owner of the house is never made clear, but she often wallops Tom (whom she usually addresses as "Thomas") with a broom when he misbehaves. She was retired from the Tom & Jerry cartoons by Hanna and Barbera in 1953 following several years of protests from the NAACP.

In 19th century Vienna, Tom and Johann Mouse live in the house of composer Johann Strauss. Whenever Strauss plays the piano, Johann comes out of his hole to dance, and Tom tries repeatedly to catch him with no success.

Goldie is a tiny goldfish who is friends with Jerry, who often foils Tom's attempts to eat her. She had major roles in Jerry and the Goldfish (1951) and Filet Meow (1966) (although the goldfish in the latter could be a different one). She also appeared in cameo roles in other cartoons such as Puss Gets the Boot (1940), Puss n' Toots (1942), Baby Puss (1943), The Million Dollar Cat (1944), Casanova Cat (1951), The Missing Mouse (1953), Haunted Mouse (1965), and The Brothers Carry-Mouse-Off (1965).

In his attempts to catch Jerry, Tom often has to deal with Spike (known as "Killer" or "Butch" in some shorts), a vicious but easily duped bulldog who is particularly disapproving of cats, but is gentle towards mice (though in his first appearance, Dog Trouble (1942), Spike goes after both Tom and Jerry.)

Tom tries to punish Jerry for drinking his milk by poisoning it, but his plan backfires when the poison transforms Jerry into a monster.

Jerry acquires a young ward: a small grey mouse called "Tuffy" or "Nibbles" depending upon the cartoon, who is left on his doorstep as a foundling baby in the 1946 short The Milky Waif. Jerry and Tuffy are also featured together in a series of cartoons set in 17th century France which feature the characters as "Mouseketeers", a term later adopted by the child cast members of The Mickey Mouse Club.

Tom frequently has to compete for Toodles' affection, often losing out to rivals like Butch and Spike. In Casanova Cat (1951), Toodles even falls in love with Jerry.