When we went to SA a few years ago we missed our connecting flight due to a series of misfortunes and mistakes. We were put on a flight the next morning but not charged any extra fees. Well my wife and I were discussing this last night and got to wondering if that's standard procedure or if we were simply "granted some kindness."

Is there a standard procedure for all airlines whos passengers have missed a connecting flight?

Depends on why you missed the flite. I have missed lots of connections due to airline issues and always got a later connecting flite and if overnight a free room and food allowance.

If you missed on your own mistakes that I think would be a different issue. However airlines seem very inconsistent on how they do things.

In my experience they will schedule you on the next available flight to your destination if it is their fault.
If over night they will put you up, typically.

Calgary just had a whole airport full stranded with no rooms available in town. Delay/Cancellation due to weather.

Airlines will get you to your destination on the next available flight.

Regarding the compensation, it depends upon the delay. If weather related, they take the high road and say we can't control Mother Nature; therefore, you're usually on your own regarding over night lodging, meals, etc. If it is their fault and mechanical related, they will typically put you up in a hotel at their expense and give you some sort of meal voucher.

We missed our connecting flight from Atlanta to Joburg, due to a delay in Las Vegas a couple of years ago and Delta put us up for the night, gave us meal vouchers, overnight kits and T-shirts, etc.