My greatest ever list

1. Kasparov

Didn't finish behind another player in any event between December 1981 and February 1991, was #1 for 20 years (1985-2005), won ten super GM tournaments in a row (1999-2002), reached a rating of 2851, scored 41-0 in wins against Leko + Shirov + Morozevich + Gelfand + Adams, 15-3 against Anand. Finished four matches against Karpov, won three and drew one, all of them played fairly early in Kasparov's career. The youngest World Champion ever. Defended multiple times against the strongest possible challengers. Won Linares nine times.

2. Lasker

Excellent results from the 1890s to the 1930s, with several wins in top tournaments. World Champion for 27 years but didn't play many title matches against the strongest opponents. Lost against Capablanca and drew against Schlechter, while he won easily against especially Janowski and Marshall. Undefeated in the 19 rounds of a very strong Moscow 1935, only 0.5 behind the 40 and 43 years younger winners Botvinnik and Flohr.

3. Karpov

A long and very successful career, with more tournament wins than any other player. His win in Linares 1994 was one of the most impressive tournament performances ever, but also the only time he was sole winner of the event (he shared first with Christiansen once). Didn't win as many top tournaments as Kasparov, and was made to work very hard for the match wins against Korchnoi in 1974 and 1978, winning both of them with the smallest possible margin. Didn't win any of the matches against Kasparov but played well in them.

4. Fischer

By far the strongest player in the world in the first years of the 1970s, when he could beat players like Larsen and Taimanov with 6-0 without a single draw. Retired after winning the title, and the probably very even match against Karpov was never played. Hard to compare with players with longer careers but his excellent results in 1970-72 should be enough to give him a top five spot.

5. Steinitz

Won every match he played from 1862 to the loss of the World Champion title against the almost 33 years younger Lasker in 1894. Steinitz played all the strongest opponents, some of them repeatedly, and won against them all until he faced Lasker and went down 5-10. Didn't play many tournaments and never impressed as much in them as in matches even if he won his fair share also of them.

6. Alekhine

Won the match against Capablanca in 1927 with a fairly convincing 6-3, and showed very impressive results in the beginning of the 1930s. Scored 13 wins and 2 draws in 15 games in San Remo 1930, and 15 wins and 11 draws in 26 games in Bled 1931. Won easily against Bogoljubow twice, but lost the title to Euwe to regain it immediately and was still World Champion when he died in 1946.

7. Capablanca

Lined up top results decade after decade and won the match against Lasker easily, but then lost the title against Alekhine. Didn't lose a game between 1916 and 1924 even if it only is a question of five events, a couple of them comparatively weak. Finished behind the twenty years older Lasker in tournaments but played on a high level until his death in 1942.

8. Botvinnik

One of the strongest players in the world from the 1930s to the 1960s. Scored 14 wins and 4 draws in 18 games in a very tough Soviet Championship 1945, and had won the same event with a huge margin also the year before. Won the World Championship in 1948 in impressive style but didn't show himself to be clear #1 after that even if he managed to draw against Bronstein and Smyslov, lose and win to the same Smyslov and Tal, before finally losing the title for good against Petrosian. Shared first in Wijk aan Zee as late as in 1969.

9. Smyslov

Repeated top results for a long period of time. Second in the World Championship 1948, won candidates tournaments with a clear margin in 1953 and 1956, won, drew and lost matches against Botvinnik. Ahead of Spassky, Petrosian and Tal in the Alekhine Memorial in 1971 (separated with over thirty years but only 0.5 point from first placed Karpov). Reached candidates final in 1984, when he was 63 years old, but lost against Kasparov.

10. Tal

Won interzonal (1958), candidates (1959) and the match against Botvinnik (1960) easily, to become World Champion at the age of 23. Uneven results over the years but for example shared first with Karpov in a very strong Montreal 1979 and won the interzonal in Riga the same year with a huge margin.

Just outside the top ten: Petrosian, Anand, Korchnoi, Spassky, Morphy, Kramnik