Best way to manage database connection for a Java servlet

What is the best way to manage a database connection in a Java servlet?

Currently, I simply open a connection in the init() function, and then close it in destroy().

However, I am concerned that "permanently" holding onto a database connection could be a bad thing.

Is this the correct way to handle this? If not, what are some better options?

edit: to give a bit more clarification: I have tried simply opening/closing a new connection for each request, but with testing I've seen performance issues due to creating too many connections.

Is there any value in sharing a connection over multiple requests? The requests for this application are almost all "read-only" and come fairly rapidly (although the data requested is fairly small).