How Many Pokémon Can You Get with Only Pokémon Green (Japan) or Blue (International)?
Assuming you do not use any glitches, the answer is 124. The Professor Oak challenge guide for (International) Blue can be found here, although I've made a shorter list of encounters below in case anything happens to the external guide.
The list of Pokémon you cannot get without trading, which equals 27 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 (4) - 10 total
- Golem, Machamp, Alakazam, and Gengar evolve by trade. Without the ability to trade, they are unobtainable.
- Two Eevee evolutions (2) - 12 total
- As you only receive one Eevee, you can only receive one of its evolutions.
- One Fossil Pokémon (2) - 14 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) - 15 total
- As you can only obtain one of Hitmonlee or Hitmonchan, you miss out on the other.
- Version Exclusives (11) - 26 total
- The following Pokémon cannot be obtained without the use of glitches or trading: Ekans, Arbok, Growlithe, Arcanine, Mankey, Primeape, Oddish, Gloom, Vileplume, Electabuzz, and Scyther.
- Mythical/Event (1) - 27 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- Outside of glitches, Mew was only obtainable via events that are no longer active.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
- Gift in Pallet Town: One starter & its evolutions (3 total)
- Walking on Route 1: Pidgey, Pidgeotto, Pidgeot (6 total)
- Walking on Route 1: Rattata, Raticate (8 total)
- Walking on Route 22: Nidoran♂, Nidorino (10 total)
- Walking on Route 22: Nidoran♀, Nidorina (12 total)
- Walking on Route 22: Spearow, Fearow (14 total)
- Walking in Viridian Forest: Caterpie, Metapod, Butterfree (17 total)
- Walking in Viridian Forest: Weedle, Kakuna, Beedrill (20 total)
- Walking in Viridian Forest: Pikachu (21 total)
Badge 1 through Badge 2 (Misty) - 47 Total Pokémon
- Walking on Route 3: Jigglypuff (22 total)
- Purchase on Route 4: Magikarp, Gyarados (24 total)
- Walking in Mt. Moon (all floors): Zubat, Golbat (26 total)
- Walking in Mt. Moon (all floors): Geodude, Graveler (28 total)
- Walking in Mt. Moon (all floors): Paras, Parasect (30 total)
- Walking in Mt. Moon (all floors): Clefairy (31 total)
- Walking on Route 4: Sandshrew, Sandslash (33 total)
- Walking on Route 24: Abra, Kadabra (35 total)
- Walking on Route 24: Bellsprout, Weepinbell (37 total)
- Walking on Route 5: Meowth, Persian (39 total)
- In-game Trade in Vermilion City: Farfetch'd: Trade your Spearow (40 total)
- Walking on Route 11: Drowzee, Hypno (42 total)
- Walking in Diglett's Cave: Diglett, Dugtrio (44 total)
- In-game Trade on Route 2: Mr. Mime: Trade your Abra (45 total)
- Evolve two Moon Stone Pokémon with Moon Stones from Mt. Moon (47 total)
Badge 2 through Badge 3 (Koga) - 105 Total Pokémon
- Walking on Route 10: Voltorb, Electrode (49 total)
- Walking in Rock Tunnel (both floors): Machop, Machoke (51 total)
- Walking in Rock Tunnel (both floors): Onix (52 total)
- Walking on Route 8: Vulpix (53 total)
- Gift in Celadon City: Eevee (54 total)
- Purchase in Celadon Game Corner: Porygon (55 total)
- Buy a Fire, Water, or Thunderstone in Celadon Department Store: Evolve Eevee (56 total)
- Buy a Thunderstone in Celadon Department Store: Evolve Pikachu (57 total)
- Buy a Fire Stone in Celadon Department Store: Evolve Vulpix (58 total)
- Buy a Leaf Stone in Celadon Department Store: Evolve Weepinbell (59 total)
- Evolve two Moon Stone Pokémon with Moon Stones from Rocket Hideout and Route 2 (61 total)
- Walking on Route 16: Doduo, Dodrio (63 total)
- Walking in Pokémon Tower (3F and above): Gastly, Haunter (65 total)
- Walking in Pokémon Tower (3F and above): Cubone, Marowak (67 total)
- Static encounter on Route 12 or 16: Snorlax (68 total)
- Fishing (Super Rod) in Vermilion City: Shellder (69 total)
- Buy a Water Stone in Celadon Department Store: Evolve Shellder (70 total)
- Fishing (Good Rod) in Vermilion City: Poliwag, Poliwhirl (72 total)
- Buy a Water Stone in Celadon Department Store: Evolve Poliwhirl (73 total)
- Fishing (Good Rod) in Vermilion City: Goldeen, Seaking (75 total)
- Fishing (Super Rod) in Vermilion City: Krabby, Kingler (77 total)
- Fishing (Super Rod) on Route 19: Horsea, Seadra (79 total)
- Fishing (Super Rod) on Route 19: Staryu (80 total)
- Buy a Water Stone in Celadon Department Store: Evolve Staryu (81 total)
- Fishing (Super Rod) on Route 24: Psyduck, Golduck (83 total)
- Fishing (Super Rod) on Route 10: Slowpoke, Slowbro (85 total)
- Fishing (Super Rod) in Viridian City: Tentacool, Tentacruel (87 total)
- In-game Trade in Cerulean City: Jynx: Trade your Poliwhirl (88 total)
- In-game Trade on Route 18: Lickitung: Trade your Slowbro (89 total)
- Walking on Route 14: Ditto (90 total)
- Walking on Route 14: Venonat, Venomoth (92 total)
- Fishing (Super Rod) in the Safari Zone (all areas): Dratini, Dragonair, Dragonite (95 total) (alternatively, purchase a Dratini in Celadon Game Corner)
- Walking in the Safari Zone (all areas): Exeggcute (96 total)
- Buy a Leaf Stone in Celadon Department Store: Evolve Exeggcute (97 total)
- Walking in the Safari Zone (Center and North): Rhyhorn, Rhydon (99 total)
- Walking in the Safari Zone (Center and North): Chansey (100 total)
- Walking in the Safari Zone (Center and East): Pinsir (101 total) (alternatively, purchase a Pinsir in Celadon Game Corner)
- Walking in the Safari Zone (North and West): Tauros (102 total)
- Walking in the Safari Zone (East and West): Kangaskhan (103 total)
- Gift in the Fighting Dojo: One of Hitmonlee or Hitmonchan (104 total)
- Gift in Silph Co. (7F): Lapras (105 total)
Badge 3 through Badge 4 (Erika) - 121 Total Pokémon
Badges 4 through 8 - 122 Total Pokémon
Badge 8 through Elite Four - 123 Total Pokémon
Post-Elite Four - 124 Total Pokémon