Old School "Tiers of play"

The idea of "tiers of play" is popular in 5th edition circles. The 5e DMG describes the following tiers:

* Levels 1-4 - Local heroes.

* Levels 5-10 - Heroes of the Realm. 

* Levels 11-17 - Masters of the Realm. 

* Levels 17-20 - Masters of the World.

The main criteria is spells; level 3, 6, and 9 spells are acquired in each tier beyond the first. These are significant steps, as the difference between levels 2 and 3 is smaller than level 3 and 4 (or at least that is the idea). Fighters get extra attacks at similar points, which is a good idea.

In old school play, there are multiple distinctions: "basic", "expert", "name level", "master", immortal", etc. There are differences between OD&D, Basic and AD&D. But overall, I think you could say that:

* Levels 1-3 are for "basic" heroes (1-3 is included in Holmes, B/X). They explore dungeons. Wilderness is too dangerous for now...

* Levels 4-8 are for "expert" heroes - wilderness explorers. Everyone has enough HP to be almost impervious to a single-hit kill from a soldier with a sword. Mages get fireball on level 5. AD&D gives extra attacks for Fighters/Warriors by this tier. Thieves get read languages.

* Levels 9-14 are for "conquerors" - domain management. Most classes gets baronies, followers, build towers, etc., at this point. Epic spells are acquired (raise dead in BECMI, teleport). Fewer HP per level (but more HP per XP). B/X stops at 14th.

Levels 15 + - are for "advanced" heroes (or "companion" rules). These guys are legends. You eventually get 9th-level earth-shattering spells such as "Wish". You can go up to 36 and beyond with BECMI but I find this unnecessary and redundant. In any case, the sky is the limit - you might become a demi-god.

As I mentioned in the link above, the maximum number of levels is purely arbitrary.

My own games usually stop at level 10 and I don't go into domain management often anyway. Dark Fantasy Basic stops at level 10, for example (avoiding the wonky HP progression mentioned above), but has some notes on going to level 36.

However, using 20 levels fits very well with the d20. And counting in fives is intuitive, so I like to think of levels 5, 10, and 15 for each tier "advancement".