I too am having a simmilar problem:
I am using mysql_connect(), since there is a ton of legacy code on a large site I am working on - and I am somewhat limited. I am getting alot of "Warning: MySQL Connection Failed: Too many connections in xxx/db.php3 on line 2" errors today, so I am not sure exactly where to turn. I was going to look into an explicit connectionion, but this doesn't sound like the route to go - help. Anyone have any tips or resources I can turn to? I am scouring the net and my books today to see what I can do - currently I store all dynamic content in text files, and just store the needed infor (ID, types, filename) in the db.
Thanks,