The torque on fasteners is very important. You can read many of the posts here and at other forms and see that many if not most posts are related to fastener problems.

All fasteners need tension, which you get from torque. Do you need to measure the torque? Many people don't, but it is important you understand how fasteners work and what is happening when you turn a wrench. Generally, fasteners should be tight. Too loose a fasteners will allow parts to move around, such as when a crank creaks on a spindle. But what is too tight? Simply failure in the fastener, either a stripped thread or a broken component. As a rule of thumb, at least in the bicycle world, most people tend to under tighten larger threads (bottom brackets, crank bolts, etc.) and over tighten small threads (derailleur wire pinch bolts, stem bolts, etc.) Also keep in mind that torque wrenches should not replace thinking.

See also Basic Thread Concepts