Long ago I did an upgrade from Business to First with Emirates at SIN when checking in for DXB. They called it an on board upgrade and charged me twice as much as a discounted First. I have never asked for one at the airport since. Always try and book a discounted First fare when I can get one, otherwise I just fly Business. Looks like I should start asking again.
Virgin also have a bidding scheme, although sadly I didn’t win in it. Generally I like to psych myself up in advance for the cabin I’m going to be flying in so the appeal of last minute upgrades is somewhat diminished.