Below is a list of events in chess in 1995, as well as the top ten FIDE rated chess players of that year.
- Garry Kasparov defeats Viswanathan Anand 10½-7½ in New York to win the PCA World Chess Championship 1995. The match swings first to Anand, when he takes a 5-4 lead and then to Kasparov, as he then wins four of the next five games and turns the tables in dramatic fashion. The match is preceded by Anand's 6½-4½ victory over Gata Kamsky in the qualifier.
- The FIDE World Championship 1996 progresses to the semi-final stage, where Kamsky convincingly defeats Valery Salov 5½-1½ and Anatoly Karpov overcomes Boris Gelfand's challenge 6-3. The final is postponed due to the lack of any sponsorship or venue.
- Kasparov wins the Tal Memorial in Riga with 7½/10, ahead of Anand (7). A strong field includes Vassily Ivanchuk, Vladimir Kramnik and Nigel Short.
- Joël Lautier wins a double round tournament at Amsterdam, with 4/6, ahead of Kasparov (3½).
- Kamsky, Karpov and Michael Adams share a three-way win at Dos Hermanas (all 5½/9).
- Kramnik is sole winner at the Dortmund Sparkassen Tournament with 7/9. Karpov finishes second on 6½.
- Kasparov wins at Novgorod (6½/9), ahead of Short, who shared second.
- The Horgen tournament is shared between Kramnik and Ivanchuk with 7/10. Kasparov can only manage fifth and Anand does not play at all, after falling out with the organisers.
- Ivanchuk is the winner at the Linares International Chess Tournament with 10/13, ahead of Karpov (9).
- Gelfand and Kramnik share victory at Belgrade with 8/11.
- Viktor Korchnoi wins at Madrid (6½/9), ahead of Salov (6).
- In the Grand Prix series of tournaments, Ivanchuk is successful in Moscow, Adams in London and Kasparov at the New York and Paris events.
- The body of Gilles Andruet, former French Champion, is found near Paris. He was the son of famous French Rally Car Driver, Jean-Claude Andruet. Three men later stand trial for his murder.
- In the world of Computer chess, Kasparov is engaged for two more 'man-machine' contests. He gains revenge for his earlier defeat to Chess Genius, beating the Pentium-run program in a 2-game rapid match, held in Cologne. The later contest against Fritz is branded a farce, when the machine's operator slips up and plays the wrong move. Referee Stewart Reuben will not allow the move to be retracted.
- Mikhail Umansky wins the 13th Correspondence chess World Championship for the period 1989-1995.
- Florencio Campomanes steps down as FIDE President. Kirsan Ilyumzhinov is appointed the new President.
- Spectators at the British Chess Championship in Swansea witness two upcoming stars take their first full titles; Matthew Sadler wins the Men's/Open event and Harriet Hunt the Ladies' Championship.
- In Modesto, California, Patrick Wolff wins the U.S. Chess Championship commemorative ring after a play-off with Nick DeFirmian and Alexander Ivanov. The title is however shared three ways. The Ladies' title is shared between Anjelina Belakovskaia and Sharon Ellen Burtman.
- Mikhail Botvinnik, leading Soviet Grandmaster and former world chess champion - May 5
- Lev Polugaevsky, leading Soviet Grandmaster and world championship candidate - August 30
- Harry Golombek, English Grandmaster, three-time British Champion, chess journalist, writer and World War II codebreaker - January 7
- Mario Monticelli, Italian chess Grandmaster and three-time national champion - June 30
- Sir Stuart Milner-Barry, English player, theoretician, writer, former President of the British Chess Federation and World War II codebreaker - March 25
- Genrikh Kasparyan, Armenian chess player and leading chess problem composer - December 27
- Gilles Andruet, International Master, former French Champion - August 22
- Nicolaas Cortlever, Dutch International Master - April 5
- Dr. Roza Herman, Polish chess master, twice the national Ladies' champion - March 7
- Mario Napolitano, Italian master and leading correspondence chess player - October 31
- Dr. Miroslav Katetov, Czech mathematician and former Prague chess champion - December 15
- Pablo Moran, noted Spanish chess journalist and writer - November ?