I guess it all depends on what airline you are flying. With SW you can check-in after 12:01 a.m. the day of your flight. This way you can get a section A boarding pass. And you are officially checked in, but you will still have to have your baggage checked in when you get there.
When we fly Song, we don't bother with the on-line check-in since we usually have luggage to check. With Song, you can't check-in on-line if you are checking anything. But, it is very easy to use their kiosks at the airport. You just stick in either a FF card or a credit card, for ID only. Then it asks you some questions in order to find the correct info. It will then print out your boarding pass and send you to the nearby luggage check-in slot. They tag your bags, you show your ID and off you go to security.
As far as other airlines, I'm not sure.