The chance of flying on one as a passenger is about gone. According to simple flying, Air China has 10 747s, one of which is its version of “Air Force One” and the other 9 are mostly used within China.
Atlas Air, which is a cargo airline, has 7 of its 747s that can be set up for passengers which it is willing to lease to an airline if one wanted it. 6 are currently set up for cargo and the 7th is leased to a contractor to move US troops across the Pacific.
Asiana (Korean) has one. It is currently parked in Taiwan waiting for the market to pick up.
Korean Air has 10. These are regularly in service and this is among one’s best chance of flying on one. They use it for Seoul to Honolulu often.
Lufthansa (German) has the most, with 27, which are in service around the world.
Max (Nigerian) has one that is regularly used to fly to Middle Eastern hubs from Nigeria.
And then there are the two special cases. Mahan (Iranian) 2 full passenger and the last “combi” (half passenger, half cargo) in service. Iran cannot purchase modern planes and has a whole fleet of 1980s era planes. It gets service parts via Egyptian middle men.
And Rossiya, (Russian) which has nine. All are grounded as they cannot overfly most western countries. Stuff I read says that many Russian planes are leased and they just won’t return them to the banks so they are careful about what countries they fly to even if allowed, to avoid the repo men; and that they are maybe 18 months from starting to run out of spare parts for Boeing and Airbus planes.