Web application attacks can take many forms, including cross-site scripting (XSS), SQL injection, parameter tampering, command injection, session management issues, cookie poisoning, directory traversal, cross-site request forgery, and buffer overflows. XSS is a vulnerability that allows malicious JavaScript code to be injected and run in a user's browser, potentially accessing data. SQL injection involves inserting SQL commands into a database query to gain unauthorized access. Parameter tampering modifies URL parameters to change expected behavior.