I got a new passport on the same day around 2 years ago. I had to make an appointment at the passport office in Philly, and pay an extra $60 (I think). I believe that there are only a few passport offices in the US that provide same-day service.
I was headed to the Bahamas on business, and my passport was expiring about 2 months after I was to return from the trip. I first thought that I would be OK, but a few days before the trip was told that I needed a passport that was valid at least 6 months after the end of my trip.
Obviously, better research on my part would have avoided this, but I was glad to find out that I could renew my passport on a moment's notice.