I suppose it's good programming style to close connections when you're done...
But as far as I've experienced, you only benefit from it if you have many different connections/querys etc in the same script or have many concurrent connections (ie heavy load). When you jump to another page mysql drops your connection, and you start a new one if that's in the new page. This is if you use mysql_connect().
With mysql_pconnect(), I think it's better to close the connections when they're no longer necessary. But I try to avoid that kind of connection, so I'm not sure. But I'm sure that there are other people here who have better knowledge of this, and they'll probably tell us...
And I think that the problem with connections in ASP lies within its session managment.
UN*X is sexy!
who | grep -i blonde | date; cd ~; unzip; touch; strip; finger; mount; gasp; yes; uptime; umount; sleep