Servlets are normal java classes and thus are NOT Thread Safe.
But that said, Java classes are Thread safe if you do not have instance variables. Only instance variables need to synchronize. (Instance variable are variables declared in the class and not in within its methods.
Variables declared in the methods are thread safe as each thread creates it own Program Stack and function variables are allocated in the stack. This means that variable in a methods are created for each thread, hence does not have any thread sync issues associated.
Method variables are thread-safe, class variables are not.