A huge thanks to Jim Ray for sharing this tip. This is so useful to me that I felt compelled to share it. Someone, at iPhoneFAQ writes:

The iPhone will store and dial extensions to phone numbers in a couple of different ways, depending on how you decide to interact with the answering system on the other end. In short, you can have a number for a contact in your iPhone's address book to also store their extension or conference call ID/password/whatever. When you place the call, a new button is present on your phone's UI which will dial the stored code. Check out the guide to see exactly how to store these and how it works.