Creating a path in a plugin to call a function

Something along the lines of this would probably do it:

function wpse21372_init(){
  add_rewrite_rule( 'your-page-regex/?$', 'index.php?wpse21372=1', 'top' );
  add_rewrite_tag( '%wpse21372%', '([^&]+)' );
}

add_action( 'wp', 'wpse21372_wp' );

function wpse21372_wp( $wp ){
  if( isset( $wp->query_vars['wpse21372'] ) && !empty( $wp->query_vars['wpse21372'] ) ){
    //You're on your custom page.
    //you may want to exit page
    //execution when you're done
    //so the rest of WordPress'
    //normal execution doesn't take
    //over from here.
  }
}

After you’re done adding that code, make sure you flush the rewrite rules by going to Settings -> Permalinks.