My D&D trivia might not be 100%, but here goes:
The original D&D game, released in 1974, had no level cap. Elves, dwarves, and halflings/hobbits had hard level caps, but humans could reach any level. The rulebook only showed advancement through the first dozen or so levels, though.
Basic D&D, which is the red box/blue box/Rules Cyclopedia version that you seem to have, has a level limit of 36. After level 36, characters had to become immortal to advance any further. The blue box was a beginner set, which has the rules for the first three levels. From there, you go on to the expert rules, which has more rules for higher levels.
AD&D, first and second edition, has rules for characters up to level 20. Even so, there's no hard limit on advancement there. Some added rules for 2nd edition set the level cap at 30, others at 40, but it was pretty easy to extrapolate beyond those levels.
D&D 3rd edition likewise has no level limits. The game is however very focused toward the first 20 levels, and things get a littlw weird once you hit epic levels.