Hiawatha's Rabbit Hunt (1941)

Bugs reads "Hiawatha" and winds up being hunted by him. IMDb.

The Heckling Hare (1941)

This time Bugs is chased by hunting dog Willoughby. IMDb.

Tortoise Beats Hare (1941)

An upset Bugs challenges the slick Cecil Turtle to a race. IMDb.

Wabbit Twouble (1941)

Elmer Fudd expects to find "west and wewaxation" during his visit to Jellostone National Park, but he sets up camp in Bugs' backyard, and the rabbit (and a neighboring bear) definitely don't have leisure in mind. IMDb.

Elmer's Candid Camera (1940)

Elmer takes up wildlife photography, but finds his subject, a rabbit similar to the later Bugs Bunny character, much too wild. IMDb.

A Wild Hare (1940)

Elmer is a dimwitted hunter who's "wooking for wabbits." Bugs proceeds to confuse, bamboozle, and otherwise humiliate the poor simp. IMDb.

Hare-um Scare-um (1939)

When a hunter learns of higher meat prices, he goes off to kill a proto-Bugs rabbit - but runs into constant obstacles. IMDb.

Prest-O Change-O (1939)

On a dark and stormy night, the Two Curious Puppies wander into an old dark house, and fall victim to the tricks of a mischievous magician's rabbit. IMDb.

Porky's Hare Hunt (1938)

Porky's Hare Hunt is a 1938 animated short movie directed by Ben "Bugs" Hardaway and an uncredited Cal Dalton, which stars Porky Pig as a hunter whose prey is an unnamed rabbit. Wikipedia.