Hackers can be classified as black hat, white hat, or grey hat based on their motives and actions. Black hat hackers illegally access systems to steal information or money, while white hat hackers, also called ethical hackers, test system vulnerabilities with permission to improve security. Grey hat hackers fall between these categories. Common hacking methods include website, network, password, email, computer, and online banking hacking. System vulnerabilities like malware, unpatched software, backdoors, privileged user accounts, and unknown bugs can be exploited by hackers to breach security. Regular software updates and limiting administrative privileges are important to reduce vulnerabilities.