YouMail is a free custom voicemail system that lets you control how your messages get handled. You can assign customized greetings to each of your contacts, so that calls from your Mom get answered differently than calls from the Rugby team. They even have a "dump" feature, which allows you to kill calls from that annoying telemarketer (or your brother-in-law) before they even get to leave a message.
You can listen to your messages on the phone, of course, or you can grab them at YouMail's website. By seeing who left messages, you can pick-and-choose which calls you need to get to right away, and which ones can wait a bit.
Another handy feature here is that you can forward your messages via email to other people who need to hear them. That means you don't have to transcribe them while passing them along to your co-workers, for instance. You can even email messages to yourself, so that you're more connected than ever.