I think the best situation for me was a flight from MIA to YYZ a few years ago after Pesach. There are three flights going in each direction. I was on the first flight in the AM on that route. I got to the gate late and they already had asked and gotten all the volunteers they needed. I asked the gate agent if I could get bumped she said no they already had people. So I waited until the last person boarded and asked again, are you sure? She asked me why, I said to stay in the warmer weather. She smiled and said sorry...but because I was polite and didn't pester her she said she was going to give me a first class seat instead for free. While getting settled in my first class seat and just before they closed the doors, the gate agent came onto the plane and asked me if I still wanted to stay in MIA, I said yes and she pulled me off the plane. She gave me 1st class on the next flight and $300 voucher. I asked if the next flight was oversold, she said yes and I asked if she could put me on the volunteer list and she did. I waited at airport until next flight and waited patiently while the they asked for volunteers, I gave my name at the end but the guy said they had enough people so i asked to check the list to see if I was on it. He said yes, so I waited. They boarded the flight I got bumped and got another $300 but only economy on the last flight as 1st was sold out. By the third flight the gate agent by the second flight recognized me and told me to stand by the counter because there was a late check in for first class. He told me that 45 min before a flight he can take the 1st class seat away from a paying customer and give it to whoever he wanted. This was 1hr30min before the flight, 10 minutes later he said "screw it the passenger is probably not coming" and gave me the first class ticket anyways.
What I learned about this experience is that a) you are more likely to be bumped if you are travelling alone. The airline doesn't like to break up itineraries if they don't have to (meaning if 5 people are booked together and one volunteers to be bumped and a single traveller volunteers and they only need one seat, they will take the single traveller.) b) If you ask nice and don't pester them then you can usually get bumped over someone else. Gate agents get stressed when they have this situation so they prefer passengers who are calm and polite and will give them better treatment in return. Also, because this situation has occurred more than once, and almost always on American, be the last to board and just before you board the plane ask them if they are sure they don't need any volunteers, for some bizarre reason this seems to always work for me. And remember being polite and friendly and having a smile, saying your pleases and thank yous goes a long way with gate agents who tend to see the worst in people who are travelling, they always like to see a friendly face.