Based solely on chess exploits (not including success in other career fields), which player has been the most financially successful?
Chess playing has never been a very lucrative occupation. The most money earned in the field of chess probably comes from prizes, and the big prizes are only awarded to the top players. I don't have a definite source, but I would say that Viswanathan Anand is probably the most financially successful, since the prizes have only increased since he began his reign as undisputed world chess champion in 2007. The prize is generally split in half, or 60-40 between winner-loser, or in similar fashion. The prize for this year's tournament will be $2.55 million, split between Anand and Gelfand. For 2010, the prize was 2 million euros, 60% of which went to Anand.