As a rule of thumb, you're generally OK if it's all the same airline (or on the same airline-alliance ticket), as they take ownership of the problem and generally at least try to do something. It may not be a good something (e.g. overnighting in the airport with no compensation, getting shunted from flight to flight on standby, etc.), but it's aimed at getting you there. Where it gets really problematic is if you have 2 tickets on different airlines, since airline B won't feel in any way obligated if airline A's actions caused you to miss B's flight, no matter where the fault was.