Compared to other European cities with about a million people living in it, Thessa has an extraordinary good criminal record. In 2001 we actually had an 13% decrease in criminal acts in town!!
You can walk almost anywhere in the city, anytime of the day or night without being threatened or harassed by anyone. You 'd better avoid the red light district west of Vardaris square, if you live in one of the very good hotels around there, just stick to the main Egnatia/ Monastiriou street and you ll be fine!!!
Be very careful when you cross streets even if the WALK ligth is on. Also, there are too many 'economic refugees' from other Balkan and ex-Soviet countries - keep your wallet in a safe place! Other than that, it is a very safe place to be.
Beware of pickpockets on public bus from city center to airport. The game of the team of three I encountered was for two to stop in front of me as I was trying to board the bus with suitcases while the third tried to take advantage of my frustration to lift my wallet. It didn't work, but it could have.