function readMore(){
	$categoryDetails = get_the_category($post->ID);
	$categoryID = $categoryDetails[0]->cat_ID;

	switch ($categoryID):

		case 1:
			$readMoreText = 'Continue reading this tutorial';
			break;
		case 2:
			$readMoreText = 'Watch screencast';
			break;
		default:
			$readMoreText = 'Continue Reading';

	endswitch;

	echo '<p><a title="Permanent Link to '.get_the_title().'" href="'.get_permalink().'">'.$readMoreText.'</a></p>';
}

The number after the case is ID of a category. To easily find out IDs of your categories simply go to the categories page in wordpress admin and by hovering over the category names you will see a link like “…wp-admin/categories.php?action=edit&cat_ID=5“.

Now simply call the readMore() function wherever you want to show the link.