There are many pests of honeybees. I will discuss a few of the larger animals. The Mid-Atlantic Apicultural Research & Extensions Consortium has a great publication on the topic http://agdev.anr.udel.edu/maarec/wp-content/uploads/2010/03/Pests_of_Honey_Bees_PM.pdf. Like Winnie the Pooh, bears love to chow down on brood and honey. Their quest for honey results in a hive being destroyed in the process. If you have encountered this problem in the past, then you can try building an electric fence or place a stout wire cage around clusters of colonies placed on a platform. Alternatively you may have to relocate your colonies as the bear may come back looking for more food.
Several other warm-blooded mammals such as skunks, opossum and raccoons like a quick snack of live bees. They will munch of the bees as they fly out of a colony. In addition, in the fall mice and moles can be a nuisance by gnaw frames and chewing on comb. This can be easily fixed by raising the hive up on a hive stand or placing a large mesh wire before the hive entrance reducing annoying small mammals and rodents.
Even stored equipment can provide a nice home for rats and squirrels. This can result in damaged and soiled frames. The soiled frames deter honeybees. Thus, when storing equipment, seal or close the hive bodies and super stacks.
The preceding pests are not too common but can and do occur. If you have had an experience with one or several of the pests please share your solution. In addition, if there is a large pest not mentioned please feel free to post your encounter.