I called the previous post "Why Dwarves Are Level-Capped" because there seem to be slightly different reasons that apply to elves. The maximum level for elven Magic-Users is 8, exactly as I implied the maximum should be for any non-human race. However, the maximum Fighter level is 4, which doesn't seem to fit the size limitation I suggested for dwarves and halflings. Elves are taller than either, so why cap them at 4?
Of course, there aren't enough official classes in the original books to suss out too many patterns, but I would suggest that the rule is: for races that can be more than one of the original classes, one class is the "primary" class for the race and is limited to 8 (or less,) while all other classes are limited to half the level of the primary. I would be tempted to add a mildly-magic barbaric race (brute elves?) that swap the two level limits: 8th level Fighter, 4th level Magic-User. Later editions that added new races willy-nilly have no such restriction and just pick arbitrary numbers as level caps, but I prefer this way.
There's another reason why elves may be limited to 8th level, though. Notice that if they were allowed to reach 9th level, elves would gain access to 5th level spells. These would include rather un-elven spells like Teleport and Telekinesis (too science fiction-y,) Animate Dead (too necromantic,) and Magic Jar and Contact Higher Plane (deal with souls or religious issues.) A couple of the 6th level spells feel very un-elven, too, like the Invisible Stalker (the original "demon summoning" spell,) Reincarnation, and Disintegrate.
In contrast, consider these very elven 4th level spells: Plant Growth, Massmorph, and Hallucinatory Terrain. Dimension Door also seems to be more in keeping with elven "teleportation" than the much mightier Teleport. Elves in the source literature are often very magical, but never seem to be as powerful as the human conjurers, necromancers and wizards, who seem to challenge reality itself.