Adolf Anderssen was the best player in the world for a lot of his life, but was never 'World Champion' because there was no official match or organisation to arrange an official match.
He was a wonderful attacking player, but lost matches to Morphy (1859) and Steinitz (1866), who both knew how to attack, but understood more than Anderssen about developing and defending. But he was a great favourite, not just among chess fans, but also chess players, for being a decent chap as well as a terrific player. Frederick Edge describes Anderssen:
"I have never seen a nobler-hearted gentleman than Herr Anderssen. He would sit at the board, examining the frightful positions which Morphy had forced him, until his whole face was radiant with admiration of his antagonist's strategy, and positively laughing outright, he would recommence resetting the pieces for another game, without a comment."
He played two of the most famous chess games ever, which I give you below. In both games, Anderssen sacrifices his Queen, and more besides!
But first here is a game against Zukertort, who played Steinitz in the first match for the World Championship. Anderssen gives up a pawn but the position becomes quite blocked. White then attacks down the g-file, and is not afraid to sacrifice to do so:
[Event "Westdeutscher SB-08.Kongress"] [Site "Barmen"] [Date "1869.08.08"] [Round "?"] [White "Anderssen, A."] [Black "Zukertort, J."] [Result "1-0"] [ECO "C51"] [Annotator "attack: g-file"] [PlyCount "65"] [EventDate "1869.08.06"] [EventRounds "5"] [EventCountry "GER"] 1. e4 e5 2. Nf3 Nc6 3. Bc4 Bc5 4. b4 Bxb4 5. c3 Ba5 6. d4 exd4 7. O-O Bb6 8. cxd4 d6 9. d5 Na5 10. Bb2 Ne7 11. Bd3 O-O 12. Nc3 Ng6 13. Ne2 c5 14. Qd2 f6 { White has space and development, but Black doesn't mean to let him have open lines.} 15. Kh1 Bc7 16. Rac1 Rb8 17. Ng3 b5 18. Nf5 {[#]} b4 19. Rg1 Bb6 20. g4 Ne5 21. Bxe5 dxe5 22. Rg3 Rf7 23. g5 Bxf5 24. exf5 Qxd5 25. gxf6 Rd8 26. Rcg1 { [#] The Queen's-side and centre are rotting away, but it almost doesn't matter because of White's attack on the g-file.} Kh8 27. fxg7+ Kg8 28. Qh6 Qd6 { [#] And a final flourish:} 29. Qxh7+ Kxh7 30. f6+ Kg8 31. Bh7+ Kxh7 32. Rh3+ Kg8 33. Rh8# {(applause) 1-0 (33) Anderssen,A-Zukertort,J attack: file - g1-g8 (Barmen) 1869} 1-0
This game, from the first ever international chess tournament, is known as 'the Immortal Game':
[Event "London 'Immortal game'"] [Site "London"] [Date "1851.06.21"] [Round "?"] [White "Anderssen, A."] [Black "Kieseritzky, Lionel Adalbert BF"] [Result "1-0"] [ECO "C33"] [Annotator "attack: brilliant"] [PlyCount "45"] [EventDate "1851.06.21"] [EventRounds "1"] [EventCountry "ENG"] {Regis,Dave: 'The Immortal Game'} 1. e4 e5 2. f4 exf4 3. Bc4 (3. Nf3) 3... Qh4+ 4. Kf1 b5 5. Bxb5 Nf6 6. Nf3 Qh6 7. d3 Nh5 8. Nh4 Qg5 9. Nf5 c6 10. g4 Nf6 11. Rg1 cxb5 12. h4 Qg6 13. h5 Qg5 14. Qf3 Ng8 15. Bxf4 Qf6 16. Nc3 Bc5 17. Nd5 Qxb2 {Regis,Dave: '[#] the most famous double-rook sacrifice of all'} 18. Bd6 Bxg1 19. e5 Qxa1+ 20. Ke2 Na6 21. Nxg7+ Kd8 22. Qf6+ Nxf6 23. Be7# 1-0
And this game is known as 'the Evergreen Game'
[Event "Top 10 combinations: Berlin 'Evergreen'"] [Site "Berlin 'Evergreen'"] [Date "1852.??.??"] [Round "?"] [White "Anderssen, A."] [Black "Dufresne, J."] [Result "1-0"] [ECO "C52"] [Annotator "Top 10: combinations"] [PlyCount "47"] [EventDate "1852.??.??"] 1. e4 e5 2. Nf3 Nc6 3. Bc4 Bc5 4. b4 Bxb4 5. c3 Ba5 6. d4 exd4 7. O-O d3 8. Qb3 Qf6 9. e5 Qg6 10. Re1 Nge7 11. Ba3 b5 12. Qxb5 Rb8 13. Qa4 Bb6 14. Nbd2 Bb7 15. Ne4 Qf5 16. Bxd3 Qh5 17. Nf6+ gxf6 18. exf6 Rg8 {[#]} 19. Rad1 $3 {burning his bridges in some style} 19...Qxf3 20. Rxe7+ Nxe7 21. Qxd7+ Kxd7 22. Bf5+ Ke8 23. Bd7+ Kf8 24. Bxe7# 1-0