I was the beneficiary of a NW overbooked F cabin in LAS about 5 years ago. I was booked on the 1am flight to MSP. At the gate, I inquired about switching my window F seat to an aisle. The agent briefly consulted with another agent who walked over and said something like "sir, we're in an unusual situation and you seem like a nice guy, here's the situation...."

I was offered a Y aisle with empty adjacent middle seat + $300 voucher and about 3 amenity packets, which I gladly accepted. They offered later flights as well if I had wanted it.

A different situation a couple of years ago, but one of the most chaotic scenes I've witnessed, was when CO downgraded a LAX-IAH flight from a 35J 764 to a 12F 753 and unattentive gate agents allowed many to board with OLCI boarding passes that no longer had correct seat assignments. The Captain spent at least 20 minutes in the cabin diffusing the situation. Many pax were very upset.