No. EEGs can be used to monitor the general mental state of a person and to diagnose disease. The kind of resolution that EEGs have, that is very responsive but with a low spatial definition, lets us examine the kind of electrical wave patterns in the brain. For example, alpha waves indicate a person being relaxed (Ref.)
Some experiments have been performed to "read" people thoughts with another tool, fMRI. This is called "thought identification" and it is not at all controversial that it is being performed, as the page I linked shows with good references.
For example IBM patented a machine to retrieve images from scans and visual images have been reconstructed in an experiment.
Even then, fMRI is tricky to use correctly, as shown by recent results and meta-analyses (Scientific American, The Scientist). This doesn't mean that the results are bogus, but that results are way harder to achieve than "reading the brain waves".