Thousands of Errors via Email! Too many connections to database!?

[King Justice]

Hello!

My site is high-traffic (I guess?). I get about 10k uniques per day to my forum and over 100k page-views from them..

I know my server can handle it:
Intel Quad Core Q6600 processor
4GB DDR2-800mhz RAM
2x 160GB 7200rpm HDD (8mb cache)

I am getting many of the following error messages via email:

Originally Posted by vBulletin Database Error

Database error in vBulletin :

mysql_pconnect() [<a href='function.mysql-pconnect'>function.mysql-pconnect</a>]: Too many connections
../includes/class_core.php on line 311

MySQL Error :
Error Number :
Request Date : Friday, August 22nd 2008 @ 01:33:24 AM
Error Date : Friday, August 22nd 2008 @ 01:33:24 AM
Script : ../showthread.php?t=[doesn't matter]
Referrer :
IP Address : [IP of user and guest at the time]
Username :
Classname : vB_Database
MySQL Version :

What do I need to tweak to fix/prevent this error? Are there PHP config settings I should change etc?

Please help me ASAP.
Thank you.