They'll often be much more accommodating than they're required to, but since you're asking about the rules, specifically, know that the rules and especially the number of hours vary by airline.
In US Airway's case, the overriding rule is this one:
"Schedules are subject to change without notice. US Airways is not responsible or liable for making connections, or for failing to operate any flight according to schedule, or for changing the schedule of any flight."
And:
"No refunds will be made for nonrefundable tickets."
Also note:
"When a ticketed customer holding confirmed reservations on a flight will be delayed because of a schedule irregularity (whether a missed connection, flight cancellation, omission of a scheduled stop, substitution of equipment or a different class of service or schedule change), US Airways will rebook the customer on its next available flight to the customers ticketed destination without additional charge. If US Airways is unable to provide onward transportation, US Airways may attempt to rebook the customer on the next available flight of another airline with which US Airways has an agreement allowing the acceptance of each others tickets."
Note that that second sentence only applies if US Airways is unable to provide alternate transportation --
not just if you don't
like what they offer to provide you.
The rules appear to limit refunds, now, only if the alternative US Airways offers is ground transportation. It seems that if they offer you an alternative flight, any time that day, no refund is necessary. However, as mentioned above, they'll often be more generous than they're required to be, so it cannot hurt to ask.
[Source:
http://www.usairways.com/common/resources/_downloads/aboutus/US_contract_of_carriage.pdf]