what kind of data is it? if it is something simple, like a list of names, you can make a php script to output the names on the remote server ( assuming it has php ), then read it from your local application.
for example, the remote php script would look something like this:
<?
$result=mysql_query("select user from users");
$num=mysql_numrows($result);
for($i=0;$i<$num;$i++)
{
echo mysql_result($result,$i,"user") . "\n";
}
?>
this will generate a text file with a username on each line.
on your local app, or wherever the script is that you want to read it, use the file() function. file() takes each line into an array.
<?
$array = file("http://remoteserver.com/script.php");
foreach($array as $each)
{
echo "$each <br>\n";
}
?>
if you have more complicated data, it will be more difficult without a direct connection to the db.