Do I need to wear safety goggles to protect my eyes when working with fiber optics?
Safety goggles are always a good idea, the only real danger when working with optical fiber, which is not connected to equipment is getting a small piece of broken fiber in your eye.  Plain safety goggles WILL NOT protect you from laser radiation.

What about laser safety goggles?
Laser safety goggles, on the other hand, can protect your eyes from dangerous laser radiation from a fiber optic transmitter’s optical port or the end of an optical fiber connected to a transmitter using a laser emitter. This light is usually at 1310 or 1550 nm which are wavelengths that are invisible to the human eye but still potentially dangerous. In addition whenever using laser based fiber optic equipment it is important to never look directly at the output from any optical port whether you have goggles or not.