Yes, cells do attack each other! Not only do single-celled (or "unicellular") organisms attack and eat each other all the time, but in your very body your cells are constantly fighting off foreign, invading cells. Amoebas, which are unicellular organisms that are commonly found all over in water, eat bacteria for food. Amoebas surround and engulf the bacteria in a process called phagocytosis. There are many other "predatory" unicellular organisms that eat other unicellular organisms through one process or another in the wild. In your body, your immune system fights foreign, unicellular invaders constantly. You immune system contains several different types of white blood cells (also known as leukocytes) that play different roles in defending your body against bacteria, viruses, and even cancerous cells. Altogether the different leukocytes can identify, mark, and destroy these invaders, as well as record their encounter in a "memory" so that your immune system can more quickly respond to a future encounter with the same invader.

Thats a great question! The biology off cells is very interesting; cells take many specialized forms and have special roles to play in organisms. The short answer to your question is yes, cells do attack each other. There are several examples of this.

Single-celled eukaryotic organisms called amoeba can hunt and engulf prokaryotic bacterial cells. Some sponges have cells that will attack another sponges cells if those cells are growing into the sponges body. Also, there are specialized cells in the immune system called phagocytes. Phagocytes can kill bacteria and other pathogens by releasing toxic gas or compounds or by swallowing the bugs up and attacking them inside the cell. Some phagocytes chop up the pathogens and display the bits on the outside of their cell membrane. These bits can be recognized by another immune system cell called a Cytotoxic T cell. These T cells are activated after they see pathogen bits displayed on the outside of other cells. Once activated, the cytotoxic T cells will attack and kill any other cells that are displaying the pathogen bits because these might be infected. Another immune system cell type is the Natural Killer cell, and these cells also patrol the body, examining the bits displayed on the outside of other cells. Natural Killer cells can recognize cells infected with viruses and even cancer cells, and will destroy these too. Unfortunately, these immune systems can sometimes go awry, and will recognize healthy self cells as foreign and will attack the bodies own healthy cells; this is called autoimmunity. These are just a few interesting examples of cells attacking other cells, but there are others, and if you are interested by the wild world of cell warfare, you can look into immune system cells more in depth; its fascinating!