Does wearing sunglasses protect your eyes while on the computer?

Maybe: If you are protecting them fro flying objects, yes. If you wish to protect them from flying dust, yes. If your goal is to protect them from radio and light waves, yes. However the waves are pretty safe. I would not recommend them unless you feel more comfortable wearing them.

Take breaks: Computers, electronic gizmos, and screen-staring can be such a huge part of our lives now. Best way to protect your eyes (and neck, shoulders, back, wrists...Really, all over): be sure to take breaks every 30 minutes. Do something different. Get up and get moving. Good luck!

Not protect, but...: If you are getting headaches from a screen that is too bright causing you to squint, sunglasses or turning down the brightness can help with this. The eyes themselves are not in danger, though.