All dogs have some level of aggression. From your dog's perspective, aggressive behavior is a perfectly valid method of communication.

1. Territorial Aggression Closely related to protective and possessive aggression. Territory can be a fairly loose description in your dog's eyes. If you regularly walk him around the block and he is urine marking along the way, he may well consider the entire block his. Protective aggression manifests when a dog feels that they need to shield his family. This often will show up when the dog does not feel that their owner(s) are not the alpha dogs in the pack. Possessive aggression occurs when a dog is protecting their food or toys. This can also show up when your dog filches from the trash and has decided that a particular tissue is important to them, especially for ripping up.
2. Redirected Aggression Many sources give an example of this slightly puzzling behavior: two family dogs are together, and both see a strange dog beyond the fence or out the window. Because they can't attack the stranger, they attack each other. This classic example of redirected aggression seems to be the dogs not having any other outlet for their aggressive instincts.
3. Fear Aggression This aggression is, on the face of it, easy to diagnose. Your dog feels threatened and gets aggressive. What is a little more complex is that your dog may well go from a specific fear response to a generalized fear. For example, if your dog was bitten once, any other dog may inspire fear-motivated aggressive behavior.

There are other reasons for aggression, but there is one primary solution to most aggressive behavior - establishing your dominance over your dog. Unless your dog, aggressive or not, understands that you are in charge of his pack, you will never successfully control its behavior.