Database Connections

I have a general question concerning databases in php. More specifically, what is the general consensus on maintaining a connection. Some of this is more than likely my ignorance. My connection stuff goes something like this ... $db = mysql_connect("localhost", "stuff", "pw") or die("Could Not Connect"); mysql_select_db("stuff",$db) or die("Could Not Select Database"); <<< Other Code Here >>> mysql_free_result($result); mysql_close($db); It seems very inefficient to open and close a database with each different page or call to that database. My question is ... Is there a better way and, if so, what is it? I guess I do not quite understand just how long a connection is maintained. I hate to write code that doesn't clean up after itself. Any suggestions are appreciate. TIA Bill