Originally Streaky was Supergirl's ordinary house cat. One day Supergirl was trying to find an antidote to green kryptonite by altering its structure. When she thought her experiment had failed, she threw it out the window.
Like most cats, Streaky was inquisitive and found the piece of what would be later known as X-kryptonite. The radiation turned him into a Supercat, giving him flight, super strength, speed, and sight. With his powers he would later become a member of the "Legion of Super-Pets," a heroic group of super animals that included a dog (Krypto), horse (Comet) and monkey (Beppo) with superpowers.
Streaky and the other super-pets faded away when comics tried to become less ridiculous, and so he was eventually retconned in Crisis on Infinite Earths. In the years after, Supergirl took in another stray house cat that she called Streaky in honour of her lost pet. This Streaky never gained powers. When Supergirl was re-introduced in 2005, Streaky was re-introduced as a normal stray housecat. This time Streaky is a female and she gets her name from being unable or unwilling to use a litter box. This cat has quite an attitude and Kara had to tame her over time.
He would make infrequent appearances in Superman related and other comic books, until the comic book/cartoon "Krypto the Superdog," in which he would become a semi-recurring character. Streaky's biggest story to-date took place in Wednesday Comics where the ongoing Supergirl strip focuses on the adventures of Kara, Streaky and Krypto. He has also appeared in Superman: The Animated Series as a house cat in the Kent Farm. He and Krypto made a cameo as inhabitants of the Bottle City of Kandor, as animals given powers when Brainiac 5 turned the sun yellow. His most recent appearance in other media was a cameo in Batman: The Brave and the Bold where he was used in an advert for Plastino's cat snacks.
Power Girl's Cat Stinky is an analogue of Streaky, as Power Girl is Kara Zor-L of Earth-2. In the issue in which Stinky is finally named he displays the same inability to use a litter box, and Power Girl too, contemplates the Streaky name.