Is it possible to read words a person thinking about via EEG headsets?
What Christiaan says true. It is sheer impossible. However, there is technology that cán "see your mental pictures". In a TED-talk by Mary-Lou Jepsen she explains how fMRI and machine learning algorithms are used to recreate viewed or imagined videos from brain activity. It is a really neat TED-talk and definitely worth watching. 

What is possible using EEG is to make a Brain Computer Interface. I discussed this topic briefly in another question (Brain-computer interface with EEG: how to name imaginary movement of a non-self object?). Hopes these answers help you somehow.