I've been using KnockoutJS quite intensely for several months now and wanted to give some quick thoughts.
First of all Knockout isn't quite as novel as it was when it was introduced several years ago. There are many, many JS front-end libraries and frameworks out there now and they are in very wide use. Let's actually address that right off the bat, Knockout is a library and not a framework. That means you can think of it more as a tool to take care of things like keeping the DOM up-to-date and templating instead of having to build your entire application around the framework. Since it is a library you can use it with or without jQuery. I used it with jQuery and found that they played very nicely together. Bear in the mind that the purpose of many of these libraries and frameworks is to take care of issues like parsing and updating the DOM structure, which means you won't be using as much jQuery as you used to, but I still kept it around for things like map/reduce/foreach on browsers that do not support the ECMAScript 5 standard (eg. IE8). Knockout makes use of the Model-View-ViewModel pattern which may be familiar to you if you've done work with WPF, SilverLight or various other MicroSoft display technologies. It also makes excellent use of the Observer pattern to intelligently track changes to the underlying data that is driving what you see on the page, even carefully managing dependencies which makes just about anything you can build with Knockout perform extremely well.
The syntax of Knockout makes quite a bit of sense as well: all elements it works with are defined by the 'data-bind' attribute. It also has a bunch of standard bindings that keep track of what is happening on the web page; things like clicking, events, focus and checking all have bindings you can easily make use of. And if Knockout doesn't have a binding that you need you can easily roll your own - I actually did this when I wanted jQuery behaviors to trigger at various times and all of this works seamlessly.
Where Knockout falls regarding its competitors is quite interesting. I did research on them before deciding to go with Knockout and as fall as libraries go the most popular option seems to be Backbone.js, which doesn't seem to contain as much functionality as Knockout (especially regarding templating) but seems to be more widely adopted and with a larger selection of add-ons. If I wasn't able to use Knockout I probably would have went with Backbone, though it's usage seems to be declining in the face of more opinionated JS frameworks.