This question is difficult to answer because jQuery, other than jQuery UI, can be useful almost everytime. jQuery UI gives you a specific set of user interface widgets and behaviours, and many people think of it as loosing a kind of freedom. On the other hand, there's definitely some connection - if you're using Prototype already, and you're looking for an UI framework, your choice is most often script.aculo.us. If you're using jQuery, why not use the official side project?