Use wp_enqueue_style based on user option in widget

This is sort of sloppy as the style will still be enqueued regardless.

In the code to display your widget, change the CSS selectors based on whether or not the user selected own style:

<?php
$prefix = $instance['own_style'] ? 'ownstyle_' : 'pluginstyle_';

//then....
?>
<div id="<?php echo $prefix; ?>selector"> ...</div> etc

A user would be able to use both a widget with custom style and one with default style this way. Enqueue your style separately in its own function.

add_action( 'wp_print_scripts', 'wpse26241_enqueue' );
function wpse26241_enqueue()
{
    if( is_admin() ) return;
    if( is_active_widget( 'My_Widget' ) )
         wp_enqueue_style( 'my_style' );
}