Everyone's coughing around me at work. Is there anything I can do to protect myself?

A few things help. If many people are coughing at work, one can wear a mask, and wash his hands often. One can ask to work from home, and to be sure to get a flu shot. One can also ask the boss to send ill employees home, to have employees wear masks, to send a memo asking employees to cough onto their sleeves at their elbows when coughing is occurring, etc... Not shaking hands is also a good idea.
Hand washing.... You need to wash your hands frequently so you won't pick up the virus or bacteria on your hands and spread it to your eyes/nose/mouth, etc. Also, do not share utensils, cups, etc and disinfect things you do share (example: telephones!). If you follow these precautions, you will decrease the chances of contracting the infection (may still catch it if you inhale airborne virus or bacteria, for ex.!).