Send data from a Drupal site to a web service
Well, it probably depends on the type of web service you want to send data to, but there is this module, REST API Query, for REST web services (http://drupal.org/project/rest_api_query).

This week we needed to send an issue report form data from a Drupal site to a Redmine issue tracker, using the Redmine web API. We played around with the above module, but finally decided to do it in plain PHP, using CURL.

Here's the code we are using (inside the custom Drupal module we made), so you can get a general idea. You can easily adapt to your specific needs.

$url = {The API url here};
$userpasswd = {api-user}:{api-pass};
$xml = {XML payload};

$ch = curl_init();
curl_setopt($ch, CURLOPT_URL, $url);
curl_setopt($ch, CURLOPT_POST, false);
curl_setopt($ch, CURLOPT_USERPWD, $userpasswd);
curl_setopt($ch, CURLOPT_HTTPHEADER, array('Content-Type: text/xml'));
curl_setopt($ch, CURLOPT_POSTFIELDS, $xml);
curl_setopt($ch, CURLOPT_FRESH_CONNECT, true);
curl_setopt($ch, CURLOPT_FAILONERROR,1);
curl_setopt($ch, CURLOPT_TIMEOUT, 15);
$result = curl_exec($ch);
curl_close($ch);


UPDATE: There is a drupal core function that performs the same task, drupal_http_request. I guess it would be better to use that one, doing it the drupal way and all :-) I have not yet tried it out though.
http://api.drupal.org/api/drupal/includes!common.inc/function/drupal_http_request