I am new to wordpress, Here i use the wordpress TwentyEleven theme, i need to customize the widget markup. It means the suppose i want to change the element 'ul' to div and add some class or id to this element. Now currently it was not possible for me because the wordpress default widgets are already available inside wordpress core file..
add something like this to functions.php:
Also... you can look at the http://codex.wordpress.org/Widgets_API examples to see how you can extend the WP_Widget class to create custom widgets that you want.
You can disable all the standard widgets easily by adding an empty text-box widget to the first widget area (see Appearance->Widgets in your admin interface).
But i don't really understand your question, can you specify what you mean? What do you want to show in the widget area?
If you just want to edit the standard widgets in the TwentyEleven theme go to the file: sidebar.php (wp-content/themes/twentyeleven/sidebar.php)