database connection pooling: overkill or essential?

Hey everyone, I've noticed a lot of focus on database connection pooling lately, especially for apps that handle tons of requests. The whole point is to keep connections open and reuse them, rather than making a new one every single time. It sounds like a no-brainer for speed, right? But I'm wondering, when does it actually become absolutely necessary, instead of just something that's good to have? Are there times when managing the pool is more trouble than it's worth? What have you all found working with connection pooling, and are there any tricky bits I should watch out for?