This is what Derick said about this (in #14149):
This is not a bug, the MySQL extension will open a new connection if the _current apache child_ has no open connection to MySQL.
With this in mind, it's very normal to see that apache has multiple connections open to MySQL.

However, this is something else. This need to be investigated first.

Assigning to myself

doh.

To fix this problem, you should set your mysql-server 
variable timeout_interactive to the number of seconds 
(default is 28800).

For pconnect use the optional 4th parameter client_flags:
mysql_pconnect($host, $user, $pass, 
MYSQL_CLIENT_INTERACTIVE);

This allows interactive_timeout seconds (instead of 
wait_timeout seconds) of inactivity before closing the 
connection. 

This new optional parameter is available in the latest 
CVS-tree.

I have the same problem running version 4.2.3 on a FreeBSD 4.6.2.
And I check the problem running this script:
<?
$con = mysql_connect('localhost','user','pass');
mysql_select_db('midb',$con);

$q = "Select * from categorias order by nombre limit 5";
$res = mysql_query($q,$con);
while($r = mysql_fetch_array($res,$con))
{
	print "<p>".$r['nombre']."</p>";
}
print "<hr>";

$q = "Select * from vinculos order by nombre limit 5";
$res = mysql_query($q,$con);
while($r = mysql_fetch_array($res,$con))
{
	print "<p>".$r['nombre']."</p>";
}
print "<hr>";
mysql_close($con);
?>

and checking the mysql client console with:
mysql> show status like "%onnection%";

and Max_used_connections incrementes like if the mysql_close didn't exists.