Shooting at zoos offers many people an opportunity to photograph exotic animals they will never get to see in the wild.  Cage bars, fences and dirty windows detract from your shots almost as much as the clearly artificial objects that are in the background.  There are a few simple things you can do to make better photographs at the zoo. 

Regardless of camera make or type, optical zoom when set to capture the largest possible image, also helps hide bars and cages from your image.  This technique works best when the bars are in shade so that the majority of the light the camera sees is coming from your intended subject.  The non optical zoom feature works by using less of the camera's sensor information and doesn't really help you eliminate the cage elements from your photo.  If you have an SLR, use the longest lens you have or the longest range of your zoom to reduce the effect of the bars.

Glass enclosures have problems all their own.  It is usually caused by light behind the camera being intense enough to reflect off of the front surface of the window.  I carry a cloth to clear the area I am shooting through, and an umbrella.  The umbrella eliminates the reflections of other people from the area my lens is peering through.  It gets balanced over my shoulder and is easily held in place via a wrist strap.

As for throwing the background out of focus to hide unwanted distractions like doors, windows, the back of the cage, or the idiot on the opposite side trying to get the animal's attention, the in camera way is dependent upon having aperture priority mode.  Set the aperture to the lowest number (which is the widest opening for the camera.  Apertures are actually the denominator (bottom number) of a ratio and that is why an f-stop of 22 is smaller than an f-stop of 8.  The larger opening causes the objects not in the area of focus to blur and that makes your subject stand out better.

Even if you don't have aperture priority mode on your camera, you can still achieve the same effect if you use Photoshop, Gimp, or another of the better post processing programs.  You do this by copying the background image to a new layer, applying a Gaussian blur to it and then use a layer mask and paint the animal back into clarity using a black brush on the mask.

Hope these tips help!