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How Many Pokémon Can You Get with Only Pokémon Blue (Japanese)?

Assuming you do not use any glitches, the answer is 126. As of this writing, a Professor Oak Challenge guide for this game is not yet written, but I've provided notes at the bottom of this page.

The list of Pokémon you cannot get without trading, which equals 25 species, is as follows:

Two Starters (6) - 6 total
As you can only select one starter Pokémon, the other two starters, and their evolutions, are unavailable; this totals 6 Pokémon.
Trade Evolutions (2) - 8 total
Machamp and Alakazam evolve by trade. Without the ability to trade, they are unobtainable. You can get Golem and Gengar via in-game trade.
Two Eevee evolutions (2) - 10 total
As you only receive one Eevee, you can only receive one of its evolutions.
One Fossil Pokémon (2) - 12 total
As you can only obtain one Fossil in Mt. Moon, you miss out on the other Fossil Pokémon (Omanyte or Kabuto) and its evolution.
One of Hitmonlee/Hitmonchan (1) - 13 total
As you can only obtain one of Hitmonlee or Hitmonchan, you miss out on the other.
Version Exclusives (11) - 24 total
The following Pokémon cannot be obtained without the use of glitches or trading: Ekans, Arbok, Vulpix, Ninetales, Mankey, Primeape, Bellsprout, Weepinbell, Victreebel, Electabuzz, and Magmar.
Mythical/Event (1) - 25 total
Outside of glitches, Mew was only obtainable via events that are no longer active.

Professor Oak Challenge Notes

Pre-Badge 1 (Brock) - 21 Total Pokémon

Badge 1 through Badge 2 (Misty) - 49 Total Pokémon

Badge 2 through Badge 3 (Koga) - 106 Total Pokémon

Badge 3 through Badge 4 (Erika) - 123 Total Pokémon

Badges 4 through 8 - 124 Total Pokémon

Badge 8 through Elite Four - 125 Total Pokémon

Post-Elite Four - 126 Total Pokémon