In the old days, before 9/11 and TSA, all the time. You could arrive at the airport 5 or 10 minutes before the plane was going to take-off, check bags and the front counter would call the gate and say, "we've got a runner!"
Then they tell you to run and I'd burn rubber to the gate and jump on the plane as they close the door behind me. Sometimes, I'd see them open the door to let someone in and then lock it again.
Those days are loooong gone. I think there are laws or TSA regs that say how many minutes before take-off you need to be checked in and at the gate, etc... Flying is just no fun anymore and a lot of it is the amount of time you have to allot for getting to the airport on time, etc. It eats up a whole day in each direction.