You may want to use the field type DATETIME. Check out MySQL's site (http://www.mysql.com) because there's a lot of tricks you can do with these fields. One of them is DATE_FORMAT() which works similar to how PHP's date() function works. You can use DATE_FORMAT() to reformat the date into something you'd like to see.
But no, you can not directly change the way the date and datetime fields are displayed in the database itself. But DATE_FORMAT() should do it...