The most frequent mammalian preditor in the UK and North America is the mouse. It will attempt to gain access to the hive in autumn as the weather becomes colder. The skull of the mouse cannot fit through a hole of 1/4 inch or 6mm so can be easily excluded.

In the UK the badger is a danger as it may knock over a hive. In Africa and Asia there are honey badgers which will disrupt a hive in order to access honey.

The North American continent has the very real threat of bears accessing hives. Electric fences are the most popular means of defence.

Sadly all continents have human thieves that steel from their beekeeping brothers and sisters. Do what you can to minimise the opportunity for such people.
Mus musculus
Ursus arctos
Meles meles
Essay on Bears
Scientific Beekeeping