I've offered to get bumped in exchange for vouchers (rookie mistake -- next time I'll insist on cash, but it did get me a flight to visit a friend), and a first-class seat on the flight to my ultimate destination.
I volunteered to be bumped from an American flight after Thanksgiving...total delay was only 1 hour, and the reward was $750. I used the vouchers to take my mom and me to London, which was on her bucket list...definitely worth the trade-off!
If your travel schedule is flexible to allow for a later flight, volunteering to get bumped from a flight is a sure-fire way to subsidize your future travel.
Last year in June, my wife and I were flying back to Chicago from Seattle. Our Southwest flight was grossly oversold. The gate attendant was offering to refund the flight and provide a $534 voucher for future travel. My wife and I looked at each other and said, "Sold!", and were only delayed by three hours.
We've been able to do this multiple times, and we almost always build flexibility into our return flights (i.e. schedule the second-to-the-last flight out) to allow for capitalizing on these types of opportunities.
In the 1990's, I was living the dream working for a Silicon Valley startup, travelling all the time. I took a $400 voucher to delay my flight for 2-3 hours. Then guess what? At that time, the vouchers were still only on paper, and like an idiot I filed it away and let it expire.
The last Sunday night flight before HIMSS from Atlanta to Orlando this year was oversold and they were looking for 5 volunteers. Almost everyone on the flight was either going to the conference, or families going to the theme parks. The price eventually got up to $1000. I was weighing the pros/cons of taking the money and doing the 6.5 hour drive, but ultimately the desire to start HIMSS on an empty sleep tank was just not there.
Luckily 5 college girls took up the offer and we got to see them taking celebratory shots in the bar as we all shuffled onto our crowded plane :)
I agree with Nick in that it used to be way more lucrative to get bumped, but not so much anymore. I have a sister who once traveled from Juneau, AK to LA and her family of 4 got bumped 3 times on that trip and walked off with 12 vouchers for future travel. Not bad for a day's work!
Many times in the good old days when the benefit was often a voucher for a ticket anywhere in continental US - very handy for late booked flights and well worthwhile. Now not os much with cash amounts being less valuable/helpful
Delta flight to Harrisburg, PA - $1,300. I ended up flying to Baltimore on another flight, drove to PA, and only ended up getting in like 90 minutes later.