How can you take advantage of an airline needing to bump people?

My experience in "bumping" is that of the onlooker, but I've seen it frequently enough.

The first time it was while we were flying from Italy to Peru via Amsterdam by KLM. Once in Amsterdam the company realised there were too many passengers and they looked for volunteers to fly to Lima via Atlanta instead of Aruba, which meant a delay of about eight hours in reaching their destination. For the hassle they offered about 500 dollars (I'm talking about 1999) and we could not take it as we were expected in Lima with no chance of informing our friends and we were travelling with an 8 year old child. The information about this offer was circulated by two people who came to the lounge and spoke to the travellers, then writing down the names of the volunteers and taking them to a different area for rebooking.

Another similar situation arose while flying from Milan to London. The plane had some technical problem prior to its arrival in Milan, so we were rebooked on the following flight (I was taking a group of students then). Obviously this meant that the flight became overcrowded and it was necessary for the company to find people willing to wait longer. I don't remember what the compensation was then and whether we were flying Alitalia or British Airways (I think the latter).

It recently happened with Lufthansa on a flight from India through Frankfurt. In this case the problem was partially caused by a strike which provoked the cancellation of a number of flights, so that the remaining ones were nightmarishly crowded: if they could have let us travel in standing position, they would have done it! Those who accepted to be rescheduled on different dates were probably the better off, because they were given the chance of one night in a hotel and the option of a reasonably timed flight; those who needed to return had to put up with various difficulties. On this occasion, being a frequent traveller helped you get a seat to go back more rapidly, and the same was true for those who held business class tickets.

The one time I actually volunteered but was not accepted because the offer lasted a few minutes was while returning from Prague via Vienna on Brussels Airlines. It was early June and we got stuck in Vienna; all of us waited for a couple of extra hours at least, and those who were chosen waited a bit more, but were offered a sum which roughly corresponded to the price of the ticket. In this case the offer was made over a loudspeaker in the gate area.