I've missed one flight - big accident caused lots of traffic on the way to the airport. They rebooked me for a later flight and didn't charge me anything - I think that's pretty standard procedure. Of course, you very well might be standby and not get on if there aren't any seats left.
As for missed connections, if it's the airlines fault (mechanical or crew issues) they'll put you up in a hotel. If the delay was due to weather, they won't do anything for you and your on your own to find and pay for a hotel. Of course, there are exceptions, but they'll almost never pay for weather related issues.