Before the invention of chess clocks, players could generally take as long as they wanted over any (or all) move. In casual chess this could be avoided by simply refusing to play a particular opponent, but in tournament chess this option wasn't available. At best you might have a rule that limited the thinking time over anyone move (eg no more than 30 minutes), but this rule wasn't always enforced.
For example, the final of the 1st American Chess Congress , played between Paul Morphy and Louis Paulsen, saw games as long as 15 hours. But based on the times listed in the tournament book, almost all the thinking time was taken up by Paulsen. In the game below, 27 of Paulsens move's took more than 10 minutes to play, while Morphy's longest think was (on move 51) was only 10 minutes. On move 52 Paulsen took 75 minutes to play Qh3. However the extra thinking time did not help Paulsen too much, as this game was agreed drawn, albeit in a position were Paulsen was still winning.
Paulsen,Louis - Morphy,Paul [C67]
USA-01 Congress Grand Tournament New York,NY (4.2), 30.10.1857
1. e4 e5 2. Nf3 Nc6 3. Bb5 Nf6 4. O-O Nxe4 5. d4 a6 6. Bd3 d5 7. Nxe5 Nxd4 8. Re1 Be6 9. c3 Nc6 10. Nxc6 bxc6 11. Qa4 Qd7 12. Bxe4 dxe4 13. Qxe4 Bd6 14. Nd2 O-O 15. Nf3 Bd5 16. Qd3 Rae8 17. Bg5 Qg4 18. h3 Qh5 19. Bd2 Re6 20. Ng5 Rg6 21. Ne4 Rxg2+ 22. Kxg2 f5 23. f3 Qg6+ 24. Ng5 h6 25. c4 Bf7 26. h4 Rd8 27. Qc2 hxg5 28. hxg5 Be6 29. Rh1 Be7 30. f4 c5 31. Rae1 Kf7 32. Rh3 Bc8 33. Kg1 Bb7 34. Bc1 Rd4 35. b3 Bd6 36. Qe2 Re4 37. Qf2 Qe6 38. Rhe3 Qd7 39. Qh4 Kg6 40. Qh3 Be7 41. Rxe4 Bxe4 42. Qe3 Qd8 43. Qh3 Qd4+ 44. Be3 Qc3 45. Qf1 Qa5 46. Qf2 Qb6 47. Re2 Qc6 48. Bc1 Qd7 49. Rd2 Qe6 50. Qe3 Qc6 51. Bb2 Kf7 52. Qh3 Qg6 53. Rh2 Qd6 1/2-1/2