For removing ‘Continue Reading’ link from wordpress TwentyTen theme, Edit functions.php in your theme folder and add the following code.

remove_filter( 'excerpt_more', 'twentyten_auto_excerpt_more' );
remove_filter( 'get_the_excerpt', 'twentyten_custom_excerpt_more' );

function sbt_continue_reading_link() {
	return '';
}

function sbt_auto_excerpt_more( $more ) {
	return '' . sbt_continue_reading_link();
}
add_filter( 'excerpt_more', 'sbt_auto_excerpt_more' );

function sbt_custom_excerpt_more( $output ) {
	if ( has_excerpt() && ! is_attachment() ) {
		$output .= sbt_continue_reading_link();
	}
	return $output;
}
add_filter( 'get_the_excerpt', 'sbt_custom_excerpt_more' );