I once was connecting at MIA to go to SJO when my AA connection arrived with 10 minutes to spare. I ran with my carry-on baggage from gate A to gate E and I arrived with 3 minutes before departure time. I so happened that the gate was open and they were waiting for me. As soon as I got in, they closed the door and we were off.

I guess it varies by dom/intl flights, airport, gate agents...