You need a Flash plugin on your browser for animations to play but most people have that plugin already since it comes with the latest browsers. If they don't have it its a relatively small download. I still however find Flash is great for making page intros, and banner ads. And if you are an aspiring cartoonist or animator this program is a must have. Flash allows you to move static images around via paths, so you can have something move across the screen without having to create a bunch of frames.
Flash renders all the in-between frames automatically.
Recently Adobe released a free beta version of a their own animation program called InMotion based on the same technology as Flash licensed from Macromedia. The program is not as powerful as Flash but some might find it easier to use. Swish3d is a new program that enables 3d development in Flash. Swift is a new Flash program that allows instant creation of some of the previously tedious Flash texts effects, like text break aparts. It is a must have if you are a Flash designer.