Bullseye (also known as Bullseye the Horse) is a non-speaking character in Toy Story 2. In the film, he is a toy modeled after a character on the fictional television show Woody's Roundup, where the characters consisted of Sheriff Woody, Jessie, Stinky Pete the Prospector, and Bullseye, who is Woody's horse. Both the Bullseye of the television show and the toy are fiercely loyal and obedient to Woody. The theme song of the show is playing on the record player when Bullseye jumps onto the disc while attempting to catch a toy snake fired from a toy boot by Woody. Bullseye is shown to loathe fights as he hides in a can when Jessie jumps on Woody. He is also upset at Woody's intention to abandon the Roundup gang to return to Andy, but grins when Woody decides to stay with the gang. When Woody ultimately decides to return to Andy's room, it is Bullseye's loyalty that causes Woody to try to get the other toys to join him. At the airport, after Bullseye escapes from Al's case, Woody and Buzz Lightyear mount Bullseye and gallop across the airfield to rescue Jessie from being sent to Japan. Although Woody gets separated from Buzz, Buzz commandeers Bullseye to follow Woody, as they are seen galloping next to the wheels of the plane Woody and Jessie are on as it heads down the runway. The mission finally ends when Woody and Jessie swing down from the plane and land on Bullseye's back right behind Buzz, seconds before the plane takes off. After the toys return home, both Bullseye Jessie come along as part of Andy's toys. Bullseye has every letter of Andy's name printed on the sole of each of his hooves.
Bullseye returns in Toy Story 3 as one of the remaining toys in Andy's room. At Sunnyside daycare, he proved his loyalty to Woody when he made clear he wanted to stay with him; but he only stayed when Woody told him to stay since Woody didn't want him to be alone in the attic. He helps with the toys' escape, and at the garbage dump was seen to be the most desperate to escape the incinerator. He is donated to Bonnie at the film's end.
Bullseye acts like a dog in many ways. Unlike most of the other toys, Bullseye cannot communicate in clear speech but sounds like an actual horse, and uses "body language" to "speak". According to a character interview that used to be up on the early 90's Toy Story website, Bullseye communicated with Jessie while in storage by tapping his hooves to yes or no questions.