If you live in the western US, I would suggest a Steller's Jay. We answer questions from around the world, so knowing where you are seeing this bird is crucial to correctly identifying it. Knowing its size would also help.
The small bird with a black head and white body is called a pied wagtail.
Red head and black body bird
The bird with a red head, white neck, and black body is a red-headed woodpecker.
brown headed cow bird
a Rook is a bird with a black head.
That would be the Black Headed Oriole.
a Common Grackle is one
This type of bird is a vulture. Vultures usually have black feathers, though, not brown.
European (or Common) Starling and the Common Grackle
Here. Type in "xeme." The bird has a black head and a white body. The tips of its wings are black.
Its a Northern Cardinal with a parasite problem. The parasite results in a loss of feathers around the head, giving it the apperance of a black head.
A mallard is a bird that has an iridescent green head and brown on the body. The ring necked pheasant is another bird with a brown body, and an iridescent green head.