It depends on what you mean by "repeat games", but even in the strictest sense of the word, repeat games have certainly happened. Here's an example of a completely repeated game:
[White "Liviu Dieter Nisipeanu"]
[Black "Gata Kamsky"]
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.c3 Nf6 5.d4 exd4 6.cxd4 Bb4+ 7.Bd2 Bxd2+ 8.Nbxd2 d5 9.exd5 Nxd5 10.Qb3 Na5 11.Qa4+ Nc6 12.Qb3 Na5 13.Qa4+ Nc6 14.Qb3 Na5 15.Qa4+ Nc6 16.Qb3
This is a well-known draw, and as Chessbase put it, there've been at least 75 games that ended this way. Still, you can't fault the players: Nisipeanu (who had White) had lost his first two games in the tournament, while Kamsky had the Black pieces and one can't ask for more than a draw with Black.
If you're thinking of "repeated" until a decisive result, then opening traps can easily yield repeated games. Here's a famous example:
1.d4 d5 2. c4 dxc4 3. Nf3 c6 4. e3 Be6 5. Ng5?? Qa5+
Black wins since the knight on g5 is lost. A list of victims of this trap is given here.
Here's another record that might be of interest. Although the game wasn't repeated in its entirety, it was repeated up to the point where a human player might have resigned. In game 64 of the superfinal of the 16th TCEC season, between top engines Stockfish & AllieStein, the engines followed a known game for 39 moves. The original game happened in 2018, between Exxon (Toltec 4 Pro)-Attakinski (Raubfisch ME262_GTZ). Playing out the position after the book line ended was rather academic, since Black is completely lost.
1. e4 e6 2. d4 d5 3. Nc3 Nf6 4. e5 Nfd7 5. f4 c5 6. Nf3 Nc6 7. Be3 Qb6 8. Na4 Qa5+ 9. c3 Nxd4 10. Nxd4 cxd4 11. b4 Qc7 12. Bxd4 Be7 13. Bd3 Nb8 14. O-O b6 15. Rc1 Nc6 16. Bf2 O-O 17. a3 Bb7 18. c4 dxc4 19. Rxc4 b5 20. Rc3 bxa4 21. b5 Rfc8 22. bxc6 Bxc6 23. Bxh7+ Kxh7 24. Qh5+ Kg8 25. f5 Qxe5 26. Rh3 g6 27. Qh7+ Kf8 28. fxe6 Qg7 29. Be3 Qxh7 30. Rxh7 Kg8 31. Rfxf7 Bf6 32. Rh6 Bb2 33. Rxg6+ Kh8 34. e7 Be8 35. Rh6+ Kg8 36. Rf8+ Kg7 37. Rhh8 Kg6 38. Rhg8+ Kh7 39. g4 Rcb8 40. g5 Be5 41. Bc5 Bg6 42. Rd8 a6 43. Kf2 Bf7 44. h3 Bg6 45. Kf3 a5 1-0