Flex is a great tool to build Rich Internet Applications (RIAs), although I wouldn't say it's specifically for websites. It is being adopted quite heavily right now by huge organizations (SAP, IBM, etc.), which I think is indicative of where it's going.
Flex is not made for animations and sprite oriented functionality, but that's where you can leverage the power of Flash and perform the necessary integration. If you're going to be developing with Flex, check out Cairngorm on the Adobe labs website, it's a nicely architected framework for building RIAs.