There are a lot of javascript frameworks; besides jQuery and ExtJS, the big ones I've looked at closely are dojo, YUI, Google's closure library, and prototype.js. And there are a bunch of others that I haven't really looked at.
jQuery's roots are in adding a bit of interactivity to a server-generated page. So if the DOM nodes in your web page are mostly coming from the server, then jQuery is absolutely the way to go in my opinion. On the other hand, if you're writing a full-blown client-side application, where you're creating most of the DOM nodes in JS code, then one of the bigger frameworks (particularly dojo, YUI, and closure) might be more suitable.
At least, that's what I would have said a few years ago. jQuery has really taken off in popularity lately, and people are adding on more and more functionality that's suited to client-side apps (like jQuery UI, for example). So even if I was writing a client-side app, nowadays I might just go with the crowd and use jQuery. Plus, more people are likely to be familiar with it, so I'd say it's a pretty safe choice.
I indeed saw that question, But in this question I am really interested in GUI widgets and I thought that that question was more into basic parsing stuff
duplicate? Bio-Javascript?