For landscapes, bracketed photos can really help you capture the best settings for reducing or overexposing the bright spots. Or you can combine the bracketed photos in HDR software, such as Photomatix.

Bracketed photos, however, are a little less effective for animals since the animals are usually moving. You can create a series of different exposures in post-processing and then combine those images to pull out the shadows and tone down the highlights. 

Recomposing the photo can also help remove or hide the bright areas. 

Ideally, a proper exposure for your photograph and avoiding the middle of the day when the sun is brightest will help reduce bright spots in your photos. Good composition will also aid in getting those bright spots out of the picture.