Responding To ActionResults With JQuery?

I know how to respond to a form post in ASP.NET MVC using jQuery, but I'm having trouble with something that is a little bit more simple.

The scenario is that there is a list of items on the screen, like an ordered list.

<ul>
<li>Item 1</li> // each will corrospond with an id.
<li>Item 2</li>

This is a crude example, of course, but the basic jist is that when the user clicks one, it will perform some server side logic... so in the controller, there is a method such as ..

public bool CheckSomething(int id)
{
// do some logic to determine if the result should be true
return true;
}

It's very simple logic, really - but it still requires database access, so I cannot do it in javascript. I need to have it hit my controller. The problem is that I want the UI to respond to this. how to exactly wire this up without using a Form.