With just the jQuery lib you cannot animate the background color. But you can animate it with the jQuery UI on top of it.
So this works fine
<!DOCTYPE html>
<html>
<head>
    <script src="http://ajax.googleapis.com/ajax/libs/jquery/1.4/jquery.min.js"></script>
    <script src="http://ajax.googleapis.com/ajax/libs/jqueryui/1.8/jquery-ui.min.js"></script>
    <script>
        $(document).ready(function(){
            $('input.login_reg_input').focus(function () {
                $(this).animate({
                    'backgroundColor': '#768'
                }, 250, 'linear', function() { });
            });
        });
    </script>
</head>
<body>
    <input class="login_reg_input">click me</input>
</body>
</html>
Some years later, here are better alternatives:
Using CSS3
jsFiddle
input.login_reg_input {
    -ms-transition: background-color 1s;
    -o-transition: background-color 1s;
    -moz-transition: background-color 1s;
    -webkit-transition: background-color 1s;
    transition: background-color 1s;
}
input.login_reg_input:focus {
    background-color: #789;
}
Using only jQuery (without jQuery UI)
jsFiddle
$('input.login_reg_input').focus(function () {
    var $elem = $(this),
        cnt = 0,
        from = {    // animate from white (reg, green, blue) 255
            r: 255,
            g: 255,
            b: 255
        },
        to = {    // to #778899 (119, 102, 136)
            r: 119,
            g: 102,
            b: 136
        };
    // interpolate "from" color to the "to" color
    $(from).animate(to, {
        duration: 1000,
        step: function(now) {
            // step is invoked for each r, g and b.
            if (++cnt % 3 === 0) {  // I want to process only when the whole triple is interpolated
                $elem.css('background-color',
                          'rgb('
                              + Math.round(this.r) + ',' 
                              + Math.round(this.g) + ','
                              + Math.round(this.b) + ')');
            }
            // confused? Just uncomment line below and you will get the hang of it
            // console.log(now, this);
        }
    });
});