So I travel a lot, and have had a number of flights canceled on me.
When an airline has to cancel a flight and re-book people on another flight they have to prioritize people. First they try and honor tickets on the un-canceled later flight. Then they rank the people on the canceled flight in order. Most people don't know it, but if you've flown with an airline more than once, you will probably have an account in their CRM system (even if you don't have a loyalty account) and you will have been give a number (British Airways call this a CIV ‘Corporate Individual Value’). The higher the number, the more important you are to the airline, this means that even if you are flying economy on a cancelled flight (and you have a high CIV number), you may be prioritised for the next flight over someone in business on the same cancelled flight.
This might all sound very unfair if you dont fly a lot or you don't often fly with the same carrier, but it is the way the system is set up.
All of the above said, I have had a couple of incidents when I have had to make "emergency" flights and the airlines are generally pretty good and do their best to accommodate you, if they can. Part of the problem is that they are probably trying to deal with a couple of hundred angry and stressed passengers, (remember they are only human), so stressed or not, your best bet is to be polite and patient, explain the problem, understand that the issue is not their fault personally, and between you and the airline, try and work something else out. This may involve transferring to a different airport, or moving down a class (rarely up), if your travel is REALLY important you often have to meet them in the middle.
With regards comments above about spending large sums with an airline, I have spent approximately £50,000 (on only my own flights, not family flights) with BA this year, and I am not at the top of their CIV scoring! To be really important to an airline you need to be spending £100,000+ per year (on your own flights). That said if you get Gold (or equivalent) it should move you high enough up the list to ensure you don't get bumped on a overbooked flight and should ensure you get re-booked on the next flight if your flight is cancelled.