It's hard to formulate lists. Of all time going by raw objective playing strength:
1.Carlsen
2.Kasparov
3.Caruana
4.Topalov
5.Grischuk
6.Aronian
7.Anand
8.Bobby Fischer
9.Karpov
10.Giri
Honorable mention: Boris Gelfand.
Based off their accomplishments towards chess:
1.Mikhail Botvinnik: Astronomically advanced opening theory and traning methods.
2.Wilhelm Steinitz: Proved the superiority of positional assessments, valuing defense, and the scientific approach in general to the romantic school's intuition and raw calculation based approach that was all about attacking (even prematurely) that allowed the King's Gambit to thrive by defeating Adolf Anderssen in the first world championship.
3.Capablanca: Drove forward advances in strategic endgames by not hurrying and excelled at schematic thinking.
4.Rubinstein: Perhaps the strongest (relative to peers! Caruana would still trounce him easily of course) player never to become world champion (though Bronstein's very close match with Botvinnik puts him up there too, though as much as I like and respect Lasker I think Rubinstein would have won a match) he was the first player to play openings with the endgame in mind!
5.Nimzowitsch: He authored My System, but wasn't simply a good writer! He has impressive wins over people such as Alekhine, Lasker, Tarrasch, and even Euwe. He pioneered some great (and acceptable but suboptimal such as the Nimzo-Larsen Attack) opening systems still in use today, most notably the Nimzo-Indian, of which Botvinnik said, "There is no refutation to this defense". I'll post a Nimzo vs. Euwe game, it is an interesting one.
6.Smyslov: His amazing grasp of endgames is simply on another level! Defeated Botvinnik for the title (though Botvinnik won a rematch). Has some excellent game collections.
7.Petrosian: Disciple of Nimzowitsch, hated conceit, was left-handed according to Botvinnik (whom he defeated for the title, until Spassky wrested it from him) and ended Fischer's 20 game winning streak!
8.Geller: This proto-Kasparov had a plus score against Fischer, excelled at sharp, complicated positions. Ironically had a minus score against Spassky. Sometimes style trumps playing strength (within a reasonable range of course, an expert or even IM and below with Geller's style would still get crushed by Fischer). Has a game collection that isn't often talked about like the popular giants (Botvinnik's three volume set, Karpov's book by Edition Olms, Alekhine's Best Games 1908-1937, and of course Fischer's 60 Memorable Games and Shirov's Fire on the Board) but is nevertheless instructive. Is in serious need of a 21st Century Edition by Russell Enterprises to get back into circulation.
9.Karpov: Has the greatest tournament record of all time, positionally on an other level.
10.Kasparov: Amazing at planning and calculation. Greatly advanced Najdorf Theory.
Honorable mention to Kramnik for his amazing upset over Kasparov and showing the world that the Berlin Wall is a force to be reckoned with!
This is (in my opinion) the top 10 greatest chess players of all time. Please do not leave comments like "Oh, I think blah blah blah should be number blah." Or anything like that. This top ten list is my opinion. I'll give also some reasoning why these players are in my top ten. I will also give a link to one of there best games.
10: Mikhail Tal (1936-1992)- He barely made my top ten with great attacking style and is widely considered one of the greatest attackers of all time. He was also world champion from 1960-61. http://www.chessgames.com/perl/chessgame?gid=1139729
9: Magnus Carlsen (1990- )- You might say that he's only the best player right now, but in our era now, we have computers and of course, that's a huge boost to Carlsen's play. He is World Champion from 2013 to now. http://www.chessgames.com/perl/chessgame?gid=1272702
8: Mikhail Botvinik (1911-1995)- Botvinik was a great all around chess player who was especially good at tactics and attack, but he was also good at everythng else. He was world champion from 1948-57, 1958-60 and 1961-63. http://www.chessgames.com/perl/chessgame?gid=1031957
7: Anatoly Karpov (1951- )- Karpov was very good at positional play and endgame play. He was also world champion for a long time, 1975-85 and 1993-99. http://www.chessgames.com/perl/chessgame?gid=1069169
6: Alexander Alekhine (1892- 1946)- One of the greatest tacticians ever, and had a great attacking style of play. Although he lived in the romantic era, he still wasn't only a great attacker, but also a positional player. He was world champion from 1927-35 and 1937-46. http://www.chessgames.com/perl/chessgame?gid=1012326
5: Paul Morphy (1837- 1884)- The first one to introduce how to play positionally, like we do now. You can go look at the chess games before Morphy's era and they were just attack, attack, attack. He was an unofficial world champion, but definitely would be a world champion if there ever was at his time. http://www.chessgames.com/perl/chessgame?gid=1233404
4: Emanuel Lasker (1868-1941)- Lasker was good at everything, and especially endgames. He was the longest world champion ever, 27 years; from 1894-1921, straight! http://www.chessgames.com/perl/chessgame?gid=1026352
3: Bobby Fischer (1943-2008)- Fischer was one of the greatest all around chess players, but also one of the craziest! Though, putting aside that fact, he was superb at everything, mainly technical play. He beat Taimanov 6-0 in one match! Also he beat Larsen 6-0 too!! He was world champion from 1972-75.http://www.chessgames.com/perl/chessgame?gid=1008361
2: Garry Kasparov (1963- )- Kasparov was probably the best attacker, even though he's not known for that. Just one of the best players ever. But truely, he's both. He was world champion from 1985-2000. http://www.chessgames.com/perl/chessgame?gid=1011478
1: Jose Raul Capablanca (1888- 1942)- Capablanca is in my opinion the greatest chess player of all time. He is known for his endgame and positional play. And was nicknamed "The Human Chess Machine" because of his simple style of play. He was world champion from 1921-27. http://www.chessgames.com/perl/chessgame?gid=1102104