Case in point, a man in Texas recently died and left all of his possessions to a trust for his dog. The man's partner had predeceased, and those possessions consisted of enough antiques and collectibles to fill ten houses. Various estate sales followed, with proceeds going to the dog's trust. And as a trust must eventually end, upon the dog's death, the remaining balance will be distributed to the man's midwestern nieces and nephews.
So yes, you can do that if you mean can I leave my stuff to my dog, or cat, or bird. Estate planning is about taking control.
Oh, and for the record, the dog above is named Lucky. Appropriate wouldn't you say!
Image credit: www.sxc.hu - free image. A random dog, which reminds me of the dogs of my childhood.