Without a doubt, the best zoo images creatively eliminate the captive elements of the animals' surroundings. It can be challenging, because it's often difficult to compose your shot without getting at least one side of the animal's enclosure in the frame.
I took this shot of an African Elephant while she momentarily stopped about ten feet in front of me. Keeping my 70-300mm lens at the far end, I composed this shot - with cables from the fence directly above and below the frame. It's a little abstract, but the texture of her skin pops and you get just enough of the ivory to identify the animal...which....isn't it just nice to see the ivory on her, where it belongs?
Another image that was difficult to take was this shot of a François Langur. The indoor enclosures are dark spaces with weird lighting and normally you have to shoot through glass. Challenging! This image was taken at ISO 6400 and it still left me with a shutter speed of around 1/15 of a second. It's a bit blurry, but for an image taken at 300mm I will take it! Off-hand, I don't remember what the recommended shutter speed is when you're hand holding a shot at 300mm, but I'd imagine it's somewhere around the speed of light.