They can.
See http://drupal.org/node/352970
The idea is to use specific names for template files, also called template-suggestions.
Some examples are:
The files views-view--alpha--page.tpl.php
and
views-view--alpha--block.tpl.php
, for instance, would control those
two types of displays for the alpha view.
The file views-view--page.tpl.php
would control all views with a "page"
display.
The file views-view--page-1.tpl.php
would control the display
on the first page of all views (for those that use a pager), while
views-view--alpha--page-1.tpl.php
would override that display for the
alpha view.
If you want more template suggestions, check out the Theme Developer. that resembles somewhat the Firebug, but allows searching for all kinds of template suggestions and theme-function naming documentation; you click on an item in your page and it shows you what names and files to use to override.
http://drupal.org/node/209561
You mentioned a list (unformatted) and a table. You will theme that, using the following files:
views-view--list.tpl.php
(overrides all lists by any view)
views-view--table.tpl.php
(overrides all tables by any view)
views-view--YourViewName-table.tpl.php
overrides the table view for that view.