The serrated knife is primarily used to slice bread or other items that require a rough sawing motion to cut through the food.
The boning knife is mostly used to dismantle and filet fish.
The chef's is the bread and butter (no pun intended) of the cook. The chef's knife can be used for slicing and chopping food into many different shapes and sizes.
The cleaver is useful for not only hacking through bones, but also chopping large amounts of vegetables or just generally impressing friends with hibachi-style flair.
The paring knife is used for intricate tasks like peeling, coring and small slicing.