What I was wondering was, if you try and use the most reliable databases possible, which player has the most number of games in those databases? Does anyone beat the 3000+ that Karpov has played? OK, I answered my own question, it seems to be Korchnoi (not that surprising). So does anyone beat Korchnoi?
Korchnoi: 4345 games
Karpov: 3454 games
Tal: 2827 games
Ivanchuk: 2635 games
Those four seem to be the ones with the most published (i.e. in databases) games.
My second question is whether there are reliable figures for number of classical games played by these players (the figures above seem to include random other games and rapidplays as well).
The third question is whether it is possible to pick out the number of classical games each world champion played while they were reigning world champion, and thus come up with a figure for the total number of games played by the generic figure of the "reigning world champion". And then play through all the games (obviously).