Reading this question I found out how changes in seat capacity are handled, which made me quite curious what kind of incentives are typically offered to people who volunteer to take a different flight.
In the US, I've experienced all the following cases:
- Upon check-in, an automated offer to change the flight. The offer might include $$ towards future travel and/or bonus miles.
- At the gate, offers of $$ certificates towards future travel. The amounts will increase sometimes as departure time nears.
- On the plane, a request for volunteers with the $$ certificates.
Sometimes they restrict volunteers to people who are not making a connection later.
Upgrading you on a later flight used to be more common but I think occurs less frequently now, as more people use miles or status to upgrade. That is, the seats just aren't available.
It's been a few years since I experienced this, but on the two occasions I volunteered to give up my seat on a plane, I was offered :-
- London to Frankfurt - vouchers of about 50% of my fare for the same airline, plus a guaranteed seat on a flight 4 hours later.
- London to Chicago - cash of about 75% of my fare, plus a guaranteed upgraded seat (premium economy) on the same flight 24 hours later. I was offered a night in a hotel too, but as I live pretty close to the airport I didn't bother to take this.
My recent experience is that airlines seem to be becoming better at not overbooking flights - the only time I have even seen requests for volunteers was when a preceding flight was cancelled due to a plane fault, but I wasn't quick enough to respond before the quota was met.
I was recently overbooked on an intra-European flight with Air France and the compensation I received was a guaranteed seat on the later flight and a redeemable voucher for a future airplane ticket booked via Air France. Having had it happen with British Airways a couple months back I would say this is common practice for domestic/European flights.
Most of the time I have encountered this, the airline was offering travel vouchers, plus accommodations if they can't get you out the same day.
I can say in the specific case you referenced, US Air was offering $400 in travel vouchers. Because we had young children, I did not inquire about it to find out what else we could get, although if we were traveling alone, my wife and I would have done it.