Basically you have to balance the cost of creating connections versus keeping connections. Even though MySQL is very fast at setting up a new connection, it still costs -- in thread setup time, and in TCP/IP setup time from your web server. This is noticeable on a high-enough traffic site. Unfortunately, PHP does not have any controls on the persistence of connections. So the answer is to lower the idle timeout in MySQL a long way (like down to 20 seconds), and to up the thread cache size. Together, this generally works remarkably well.
On the flip side, your application needs to respect the state of the connection. It is best if it makes no assumptions about what state the session is in. If you use temporary tables, then using CREATE IF NOT EXISTS and TRUNCATE TABLE helps a lot, as does naming them uniquely (such as including as userid). Transactions are bit more problematic; but your code can always do ROLLBACK at the top, just in case.
