Do not downplay the importance of avoiding the re-invention of the wheel. You don't invent a new computer each time you want to write a new program.
But apart from that, JavaScript libraries provide better cross-browser support. This is extremely helpful, as a quick look at QuirksMode will demonstrate.
JavaScript frameworks make many things easier. Look at the jQuery documentation and you will see how easily it is do many fancy things.
JavaScript frameworks have been extended by many people, so there are many high quality jQuery plugins (for example — it's the framework I know the best) that you can use without having to write them yourself.
It is unlikely that JavaScript frameworks would introduce security holes, as they don't expose any more functionality than what you can do with plain JavaScript.