jQuery input button click event listener

More on gdoron's answer, it can also be done this way:

$(window).on("click", "#filter", function() {
    alert('clicked!');
});

without the need to place them all into $(function(){...})

$("#filter").click(function(){
    //Put your code here
});

First thing first, button() is a jQuery ui function to create a button widget which has nothing to do with jQuery core, it just styles the button.
So if you want to use the widget add jQuery ui's javascript and CSS files or alternatively remove it, like this:

$("#filter").click(function(){
    alert('clicked!');
});

Another thing that might have caused you the problem is if you didn't wait for the input to be rendered and wrote the code before the input. jQuery has the ready function, or it's alias $(func) which execute the callback once the DOM is ready.
Usage:

$(function(){
    $("#filter").click(function(){
        alert('clicked!');
    });
});

So even if the order is this it will work:

$(function(){
    $("#filter").click(function(){
        alert('clicked!');
    });
});

<input type="button" id="filter" name="filter" value="Filter" />

DEMO