you can either do what CreativeLogic told you.
and add it like this.
Code:
<?php
str_replace('<p>', '', the_excerpt());
str_replace('</p>', '', "the_except());
?>
that would strip both <p> and </p> tags...
although something a little more productive would be to use regexp.
Code:
<?php
$str = preg_replace('^<p\>(.+)\<\/p\>^', '$1', the_excerpt());
echo $str;
?>
although the preg_replace will only work if the_excerpt(); has a return value not an echo value.
hope this helps some.