I've heard of others using connection pooling but have never gone for it. I have read about problems where certain things can get left around or intermingled among users that shouldn't be. For example, a database transaction that doesn't cleanly close: the next user can walk right into the middle of it.

I'm sure it saves some time, but so far the speed-up hasn't seemed worth the risk, and I've been at it for about a decade. We use one server for few thousand corporate users a day, and everything is usually fast. When things are noticeably slow, it is usually from a page loading too much JavaScript, images, etc., that it doesn't really need. When it's the database, it's because of a poorly written query taking a few seconds. Rewriting the query resumes normal operations: split-second page loads.