Why do so many clothing brands have animals in their logos?

An animal illustrates characteristics a brand can relate. Interestingly, besides animal's characteristics, all these companies have a history and culture behind their brand. History of some of these brands is dissected below:

Abercrombie & Fitch: The company is about 120 yrs old and focused on a very different market segment for a very long time. The brand was famous amongst audience that liked adventures, trekking and specially hunting till late 1990s. It sold more than just apparels - Guns, holsters, fishing and excursion equipments, hence the moose as logo. It went bankrupt in 70s and was sold to a sporting company and then to "The Limited". In 1996, it completely changed its target audience and design orientation to attract teens and older teens.

Puma: In 1948, after its spun-off from Adidas, the German based company wanted to paint a picture of its strong and bold image which gave birth to Puma. It represented "Strength" as Adidas stood for sports rigor and endurance.

Polo Ralph Lauren: The company wanted to associate itself with a Sport and there Polo was associated with their brand during its inception to represent the theme. As the company wanted to broaden its market beyond their positioning and association with Sport, it just remained Ralph Lauren. The focus was on sport and never the horse.

American Eagle: The brothers (Jerry and Mark Silverman), when they founded the company in 1977 in Pittsburgh, wanted a prominent and patriotic symbol of America to be their brand name. American Eagle, as the native national bird of America became a perfect inspiration and fit for the brand name and the silhouette of eagle became their logo.

Banana Republic: The company started small as a creative fashion and travel adventure clothing company and themed on jungle and safaris. Lacking funds for store decoration, they painted walls in Zebra strips and adopted jungle theme that also gave birth to the elephant logo. Business grew quickly and Banana Republic was acquired by The GAP. The image of the company was transformed later as a luxury clothing brand. 

That said, animals and birds have unique associated and assorted characteristic as celebrities that can be aligned to support brand image.