Validate fields using JQuery validation without any submit?

Firstly, and most importantly, you must wrap your input elements inside <form></form> tags for the jQuery Validate plugin to operate. However, a submit button is not required.

Secondly, you can programatically trigger the validity test of any or all elements without a submit button by using the .valid() method.

$(document).ready(function() {

    $('#myform').validate({  // initialize the plugin on your form.
        // rules, options, and/or callback functions
    });

    // trigger validity test of any element using the .valid() method.
    $('#myelement').valid();

    // trigger validity test of the entire form using the .valid() method.
    $('#myform').valid();

    // the .valid() method also returns a boolean...
    if ($('#myform').valid()) {
        // something to do if form is valid
    }

});

DEMO: http://jsfiddle.net/URQGG/

You will have to wrap your fields within a form to use the validation plugin and it's a good practice anyway. Also, you can invoke the plugin's validation programmatically and check if the form is valid by doing:

var $form = $('#your_form'),
    validator = $form.validate({...});

//validate the form
validator.form();

//check if the form is valid 
if ($form.valid()) {
    //form is valid
}

For more options, have a look at the docs.