Feel free to fill in any blanks I may leave or correct factual errors or omissions. This article is mostly about the "official" World Champions, beginning with Steinitz.

WCH = World Champion or World Championship Match

Pictured, L to R: WCHs Euwe, Smyslov, GM Keres, WCH Botvinnik, GM Reshevsky at the 1948 WCH Tnmt played at the Hague and in Moscow.

The Champ who played the most other champs (9) is Botvinnik, who played Lasker, Capablanca, Alekhine, Euwe, Smyslov, Tal, Petrosian, Spassky and Fischer.

The record for beating the most champs belongs to Paul Keres (9) - same list as above. He also drew Karpov twice, so he probably holds the record for playing the most WCHs of any GM

The WCH who never played a game after winning the title: Bobby Fischer (1972-1975)

Least educated WCH: Bobby Fischer was a High School dropout. His alleged IQ of 180 is a typical urban legend that gets constantly repeated by writers with no fact-checking abilities, but he appeared to be self-educated according to Frank Brady's book Endgame: Bobby Fischer's Remarkable Rise and Fall"

Most educated WCHs: Dr Lasker and Dr Euwe both had a PhD in math, and Dr Botvinnik had a PhD in electrical engineering. Karpov has a PhD in economics from Leningrad University.  Anand has an honorary PhD.  Petrosian had a PhD from Ereven State Univeristy.

Where did they come from? Steinitz (Austria, although he was a US citizen when he won the official title in 1886), Lasker (Germany), Capablanca (Cuba), Alekhine (Russia, but moved to France after WW 1), Euwe (Netherlands), USSR champs: Botvinnik, Smsylov, Tal (Latvia), Petrosian (Armenia), Spassky, Karpov, Kasparov (Azerbaijan SSR, Soviet Union);  Fischer (USA) Kramnick (Russia), Topalov (Bulgaria), Anand (India); the "disputed champs" Khalifman (USSR - Russia), Pomonariov (Ukraine) and Kasimdzhanov (Uzbekistan)

WCH Clean Sweeps: Lasker NY 1893 +13 -0 =0; Capablanca, NY 1910 +7 -0 = 0; NY 1913 +13 -0 -0; Fischer US CH 1963-4  +11 -0 =0

WCHs who won 2 Interzonal Tnmts: Smyslov (1953 and 1956), Spassky (1965 and 1968), Fischer (1962 and 1970).

WCHs who played the most games vs another WCH: Karpov and Kasparov hold the record with +200 games against each other. Karpov has played Korchnoi 99 games 74 match games and 25 tnmt games  In third place is Botvinnik and Smyslov, with a measly 98 games vs each other

WCH who won the most tnmts: Karpov, 120. Kasparov won 63. Karpov has also won 40 blitz, rapid and blindfold tnmts.

WCH Dry Spell: In 1966 WCH Petrosian beat challenger Spassky - the first time a WCH had won a title match defending his title in 32 years since Alekhine beat Bogolybuv in 1934  Before that Lasker had beaten Janowski in 1910 beginning another dry spell of 19 years that ended when Alekhine beat Bogolybuv in 1929.

USA dry spell: In 1982 GM Seirawan became the first US player to beat a reigning WCH in a tnmt game - 45 years after Dr Fine beat Alekhine at Margate in 1937. NOTE: Fischer NEVER defeated a reigning WCH in a tnmt game.

The first "official" WCH is Wilhelm Steinitz, who beat Zuckertort in 1886 in the first "official" WCH title-match. Unofficially Steinitz is considered the champion as of 1866 when he beat Adolph Anderssen in an unofficial WCH title-match.

The first US WCH: was  Wilhelm Steinitz (born in Austria), who moved to NY in 1883, became a US citizen in 1886 and lived there until his death in1900. The first official WCH was played in the US between Steinitz and Zuckertort in 1886. Fischer was the first native-born US WCH.

Youngest WCH(?): Ruslan Ponomariov in 2002 won the FIDE WCH at age 18. (See WCHs who won their titles in tnmts below)

The youngest (undisputed) WCH was Gary Kasparov, who won the title in 1985 at age 22. Tal was 23 when he won the title in 1960.

Youngest Women's WCH: Hou Yifan of China became the youngest ever women’s world champion at the age of 16 in 2010. Maya Chiburdanidze, born January 17, 1961,had been the youngest women’s world chess champion in 1978 at the age of 17. (courtesy of billwall)

Youngest GMs who became WCH: Petrosian, 23 in 1952; Spassky, 18 in 1955; Fischer 15 1/2 in 1958; each GM here was the youngest GM ever when they were awarded the title.

The oldest players to win the WCH were Bovinnik, who regained the title from Tal in 1961 at the age of 50, and Steinitz, who officially won the WCH title in 1886 at age 50.

The oldest WCH: Steinitz, 58,  lost his title to Lasker in 1894

The first WCH to regain his title was Alekhine, in 1937 when he beat Max Euwe after losing the title to him in 1935

WCHs and challengers: Back in "the good old days" before Alekhine's death in 1946 left the title in the hands of FIDE Champions were free to play and avoid whoever they felt like for any reason or no reason at all. For instance, Alekhine played a rematch with Bogolybuv in 1934 instead of playing a more serious contender such as Flohr or Capablanca. In 1935 he played Euwe who was certainly a contender but probably seen by Alekhine as a pushover, especially compared to players like Flohr, Capablanca, Keres etc. However, Euwe unexpectedly beat Alekhine but  promptly agreed to a rematch in 1937 demonstating the type of sportsmanship Alekhine never showed Capablanca after beating him in 1927.

In 1938 FIDE stipulated that the winner of the AVRO International Tnmt would get to play Alekhine for the WCH, but he simply refused to play the match (vs Keres).

After dethroning Kasparov in 2000 Kramnick (as PCA champion not answerable to FIDE) avoided a rematch despite the fact that Kasparov was still ranked #1 until 2004, and still winning tournaments ahead of Kramnick and beating him at least once in a tournament.

On the other hand, in 1892 Steinitiz was given the unique opportunity of picking his own opponent for a WCH title-match, and he promptly selected the Russian master Chigorin, who was widely considered to be the strongest player after Steinitz.

WCHs and Nazis: Alekhine, former challenger Bogolybuv and future WCH candidate Keres all played in Nazi-sponsored tnmts during WW 2;  Euwe did not. After the war Alekhine denied charges of writing anti-semitic nazi propa ganda, or allowing his name to be placed on such writings; the jury is still out on this one  http://www.chesshistory.com/winter/extra/alekhine.html

The highest rated WCH ever was Kasparov, who peaked at 2851.

The WCH ranked #1 in the world for the longest time was also Kasparov, who was ranked #1 for 263 months (+21 yrs) according to chessmetrics.com

The most "over-rated" WCH compared to  his peers was Bobby Fischer: at the start of his WCH vs Spassky in 1972 Fischer was ranked #1 in the world with a 2785 rating, 125 pts higher than the #2 ranked Spassky's rating of 2660.

WCH with the longest non-losing streak: Between October 23, 1973, when he lost a game in a Soviet championship, and October 16, 1974, when he lost to Kirov at the Novi Sad tournament, Mikhail Tal had a string of 95 tournament games without a loss (46 wins and 49 draws) (Soltis 2002, p. 44) (Tal 1976, p. 500). Tal also has the second-longest unbeaten run in top-level competition. He went unbeaten in 86 games from July 1972, when he lost to Uusi in the tenth round at Viljandi, until April 1973, when he lost to Balashov in round two of the USSR Team Championship in Moscow. This streak included 47 wins and 39 draws (Tal 1976).

José Raúl Capablanca famously went eight years without a loss (1916 to 1924, including his World Chess Championship 1921 victory over Emanuel Lasker), but this was "only" 63 games

Longest winning streak vs GMs: 20 (or 19, read on) by Bobby Fischer in 1970: he won his last 7 IZ games, beat Taimanov (ranked #10) +6 -0 =0 in the Candidates Quarter Final Match and Larsen +6 -0 =0 in the Semi-Final Match and won the first Final Candidates Match Game vs Petrosian, who broke his streak the next game with a win. One of the 7 IZ games "won" was a forfeit vs GM Panno who refused to play under protest (of something or other) although Bobby tried to convince him to play.

Longest (official) reign as WCH: Dr Lasker, 26 years 337 days 1894-1921.

Longest reign (unofficial/official) Steinitz, 28 years 1866 - 1894.

Shortest reign as WCH: Tal was world champion from May 7, 1960 to May 12, 1961 (1 year and 5 days) - thanks billwall!

WCHs who were also won the Jr WCH: Spassky (1955), Karpov (1969), Kasparov (1980) and Anand (1987)

WCH who was also the World Amateur Champ: Max Euwe (1935-7) won the amateur world chess championship in 1928 and coincidentally is considered by many to be the only "amateur" WCH in that he was not a full-time chess professional 

The only WCH to also win the Sr WCH is Smyslov, who won the title in 1991.

The only WCH to die in office was Alekhine, in 1946.

WCHs who resigned their title:  Fischer, in 1975 after FIDE refused to agree to every one of his demands for a match vs Karpov inc a stipulation that he retain the title in case of a drawn result. Lasker resigned his title to Capablanca in 1920 prior to their match but no one really took him seriously, even though he stipulated he be listed as the challenger in the  match.

The first WCHs to be officially designated Grandmasters by FIDE were Botvinnik, Euwe and Smyslov along with 24 others in 1950 inc Rubinstein, Fine, Keres, Reshevsky, Bronstein, Duras, Kotov etc.

The only WCH who was also became President of FIDE was Max Euwe (1970-1978). In 2010 Karpov ran for President of FIDE with the support of his former arch-rival Kasparov but lost to Kirsan Ilyumzhinov in a devastating 95-55 defeat.

Giants among WCHs: Kramnick and Smsylov, at 6' 8' are the tallest WCHs that I know of. Who was the shortest? (I really don't know)

WCHs who never successfully defended their title: Capablanca, Euwe, Botvinnik, Smyslov, Tal and Fischer.

Longest Title Matches: The 1927 WCH was "open-ended" by requiring the winner to win 6 games, draws not counting. It took Alekhine 34 games to beat Capablanca +6 -3 =27. This record stood for 57 years before being broken in the 1984 WCH (48 games total) played under the same rules by WCH Karpov and challeger Kasparov. With Karpov leading +5 -3 =40 FIDE President Campomanes called the match off by declaring it had become a contest of endurance not skill, which was lucky for Karpov who had just coincidentally lost the last 2 games and was hospitalized immediately after the match.

Shortest Title(?) Match: was 10 games between WCH Dr Lasker and challenger Carl Schlecter in 1910. Some sources deny it was a WCH match and the circumstances surrounding it remain unclear. Leading +1 -0 =8 Schlecter "the drawing master" inexplicably played for a win in the last game and lost the game as well as his shot at the title.

WCHs who died in abject poverty: Steinitz (NYC 1900), Lasker (Mt Sinai Hospital, NYC 1941 as a charity patient. Coincidentally his successor Capablanca also died there in 1942, but he wasn't impoverished), Alekhine (Lisbon 1946) Smyslov, (Moscow 2010.)

WCHs who won their title in a tournament: Botvinnik (1948), Alexander Khalifman took the title in 1999, Anand in 2000, Ruslan Ponomariov in 2002 and Rustam Kasimdzhanov won the event in 2004. Some chessplayers consider all of the "tournament" WCHs to be "pretenders to the throne" with the exception of Botvinnik of course. Khalifman was ranked #44 when he became WCH, Ponomariov #19 and  Kasimzhanov was ranked #19 in the world in 2002.

WCHs who were won blitz WCHs: Fischer (1970), Kasparov (1987), Tal (1988), Anand (2000)

WCHs who were also rapid chess champions: Kasparov (2001), Anand (2003)

What else did WCHs do? Most of them were/are full-time chess professionals, probably the most common "part-time" job is being a chess journalist. Capablanca was a "roving ambassador" for Cuba with very few diplomatic duties, the job was mostly a sinecure to help support Cuba's most famous citizen. Botvinnik was also an electrical engineer, probably to avoid the fate of Steinitz and Lasker who both died in poverty. Anderssen (who Morphy beat for the title in 1858) and Dr Max Euwe were both full-time professors and were not chess professionals.

What did WCHs do after losing the title? Most of them continued playing chess constantly or at least sporadically. Notable exceptions include Morphy, who after retiring from chess in 1862 did nothing until his death in 1884; Botvinnik who retired in 1970 to become a pioneer in computer chess and founded a chess players school whose students included Karpov and Kasparov; Fischer quit chess in 1975 to become a full-time anti-semite, weirdo and part-time homeless person who replayed his old rival Spassky in 1992 and after spending several months in a Japanese jail was deported to Iceland where he died in 2008 at the age of 64. Karpov mainly plays blitz chess nowadays and continues to promote chess while Kasparov became a political activist, a contributor to the Wall St Journal (writing about politics not chess), coached  Magnus Carlsen for awhile and created Kasparov's chess foundation which he's active in to promote the game.

Always a bridesmaid but never a bride: Players who  played in WCH matches and never won the title inc the great Russian master Chigorin, who lost twice to Steinitz in 1889 and 1892 (thanks kosiu_drumev for reminding me here); vs Lasker: Marshall (1907), Tarrasch (1908) Schlecter (1910), Janowski (1910); vs Alekhine Bogolybuv lost in 1929 and 1934; in 1948 Keres and Reshevsky played in the WCH Tnmt (won by Botvinnik);  in 1950 Bronstein drew Botvinnik who retained the title; Korchnoi lost to Karpov in 1974, 1978 and 1981 and yes, the 1974 match was for the WCH in effect since the winner (Karpov) was crowned WCH after Fischer resigned the title. In 1993 Short lost to Kasparov in their PCA WCH title-match and Timman lost to Karpov in the FIDE WCH; In 1996, Gata Kamsky played a 20-game match against Anatoly Karpov for the FIDE World Chess Championship 1996 title at Elista in Kalmykia, losing 7½–10½ (+3=9−6); in 2002 Peter Leko drew the WCH title-match vs Kramnick, who retained his title and in 2012 Gelfand lost to Anand.

Strongest player who never competed for the WCH: I nominate the great Polish GM Akiba Rubinstein, who won 5 major tnmts in 1912 outperforming Capablanca and setting a record that lasted until 1970 when Fischer and Larsen each won 7 major tnmts.

And more: lots of fascinating stats at http://www.chessmetrics.com/cm/

https://en.wikipedia.org/wiki/Methods_for_comparing_top_chess_players_throughout_history