[jquery] how to check if input field is empty

As javascript is dynamically typed, rather than using the .length property as above you can simply treat the input value as a boolean:

var input = $.trim($("#spa").val());

if (input) {
    // Do Stuff
}

You can also extract the logic out into functions, then by assigning a class and using the each() method the code is more dynamic if, for example, in the future you wanted to add another input you wouldn't need to change any code.

So rather than hard coding the function call into the input markup, you can give the inputs a class, in this example it's test, and use:

$(".test").each(function () {
    $(this).keyup(function () {
        $("#submit").prop("disabled", CheckInputs());
    });
});

which would then call the following and return a boolean value to assign to the disabled property:

function CheckInputs() {
    var valid = false;
    $(".test").each(function () {
        if (valid) { return valid; }
        valid = !$.trim($(this).val());
    });
    return valid;
}

You can see a working example of everything I've mentioned in this JSFiddle.