The four js libraries that get the most attention are prototype, jquery, dojo and YUI.
ext js is more a widget/UI library but it has it’s own base library, it’s even possible to use other libraries to work together wit ext js
The prototype widget/UI library is called scriptaculous (although they are seldom used separately because scriptaculous extends prototype on a basic level), the jquery widget/UI library is called jquery UI.
dojo and ext js are similar in idea but they differ by functionality and workflow.
YUI is not only a js library but also a css library.
If you really want to do some javascript coding you should try them all and feel which suits you the best.