This happened to me a couple of years ago heading to JAX from BWI. I had a layover in ATL. My flight from BWI left 20 mins late (I had 40 min layover). We landed with 10 mins to spare and myself with about 5 others had a tight connecting times, so we got together (I knew no one else on the plane) and planned out our exit. By the time we got to the gate and out, they had closed the door on my next flight. I was directed over to the agent (and there were about 20 people in front of me in line). They got me on the next flight that had room on it. I sat in the Atlanta airport for 3 hrs until I got on the next plane. This was Airtran, but as other have said, other airlines will do the same.