Compulsive hoarding (or pathological hoarding) is a term which is used to describe extreme hoarding behaviour in humans. It involves the collection or failure to discard large numbers of objects even when their storage causes significant clutter and impairment to basic living activities such as moving around the house, cooking, cleaning or sleeping. Hoarding rubbish may be referred to as syllogomania.
Whilst there is no definition of compulsive hoarding in accepted diagnostic criteria (such as the current DSM), Frost and Hartl1 provide the following defining features:
the acquisition of, and failure to discard, a large number of possessions that appear to be useless or of limited value
living spaces sufficiently cluttered so as to preclude activities for which those spaces were designed
significant distress of impairment in functioning caused by the hoarding
The following case study is taken from a published account2 of compulsive hoarding:
The client, D, lived with her two children, aged 11 and 14, and described her current hoarding behaviour as a 'small problem that mushroomed' many years ago, along with corresponding marital difficulties. D reported that her father was a hoarder and that she started saving when she was a child. In addition to hoarding, she reported several other obsessive-compulsive symptoms, such as fear of hurting others due to carelessness, an over-concern with dirt and germs, a need for symmetry and a need to know or remember things. D also suffered from a handwashing compulsion and engaged in lengthy cleaning rituals of household items. The volume of cluttered possessions took up approximately 70 per cent of the living space in her house. With the exception of the bathroom, none of the rooms in the house could easily be used for their intended purpose. Both of the doors to the outside were blocked, so entry to the house was through the garage and the kitchen, where the table and chairs were covered with papers, newspapers, bills, books, half-consumed bags of chips and her children's school papers dating back ten years
Animal hoarding is a human behaviour that involves the keeping of higher than typical numbers of animals as pets without having the ability to properly house or care for them, while at the same time denying this inability  (http://www.tufts.edu/vet/cfa/hoarding/abthoard.htm#A1). Along with other compulsive hoarding behaviours, it is linked in the DSM-IV to obsessive-compulsive disorder and obsessive-compulsive personality disorder  (http://www.tufts.edu/vet/cfa/hoarding/mental.htm).
Animal hoarding can lead to serious dangers to health, both for the pets and the owners, because of the sanitation issues that keeping animals entails.