A few Pokemon in Red and Blue can only be obtained once in a fixed location. Some appear in the overworld, some are given to you, and some you must make a choice for. As these games don't have the breeding feature introduced in the second generation, this is the only way you can nab any of these Pokemon on your own version, so be weary.

Like all other Pokemon games, Red and Blue offer a few one-shot opportunities to catch Pokemon that the player can see in the overworld. With the exception of one of these Pokemon, it is the expectation that the player catches them the first time he or she encounters them - running away or defeating them will cause them to disappear forever, should the player forget to save before the battle.

#001 Bulbasaur, #004 Charmander, #007 Squirtle

Location: Pallet Town

Method:
The starting Pokemon of the game, received from Prof. Oak at Pallet Town. Bulbasaur is Grass/Poison, Charmander is Fire only (but evolves into Charizard, who gains the Flying type as well), and Squirtle is and always will be a Water only. All three are great choices, but be warned that Charmander will be difficult to manage in the first two gyms. Your rival will always pick the Pokemon of the superior type.

Bulbasaur
Level 5
OT:Yours
ID:Yours
Tackle
Growl
Charmander
Level 5
OT:Yours
ID:Yours
Scratch
Leer
Squirtle
Level 5
OT:Yours
ID:Yours
Tackle
Tail Whip
#106 Hitmonlee & #107 Hitmonchan

Location: Saffron City

Method:
Received at the Fighting Dojo gym in Saffron City after the Karate King is defeated. Both are Fighting-types and work well on any team, especially against Lorelei of the Elite Four's Ice-types and Bruno of the Elite Four's twin Onix. Hitmonchan learns the three elemental punches as well as a few other fist-based moves, though the former are useless on a Pokemon with such a terrible Special stat. Hitmonlee is more kicking oriented and will learn high risk attacks like Jump Kick that have a terribly high base power.

Hitmonlee
Level 30
OT:Yours
ID:Yours
Double Kick
Meditate
Hitmonchan
Level 30
OT:Yours
ID:Yours
Comet Punch
Agility
#131 Lapras

Location: Saffron City - Silph Co

Method:
Given at Saffron City in the Siph Co. room with your rival, Lapras is an extremely capable Pokemon. Water/Ice-type, it learns many powerful attacks like Blizzard, Surf, Thunderbolt, and Psychic. It is recommended that you use Lapras if you want a sturdy Water Pokemon with a good moveset.

Lapras
Level 15
OT:Yours
ID:Yours
Water Gun
Growl
#133 Eevee

Location: Celadon City

Method:
The backdoor of the Celadon Mansion leads to a secret entrance with several flights of stairs. At the very type there's a room where an Eevee awaits, an extremely flexible Normal-type Pokemon. What makes Eevee so special is that it can evolve into three different Pokemon: Flareon, the Fire-type, Vaporeon, the Water-type, and Jolteon, the Electric-type. The method of evolution is via stones, which can be bought on the 4th floor of the Celadon Department Store. Flareon has great Attack and Special, Vaporeon has excellent HP and Special, and Jolteon has superb Speed and Special. A welcome addition to any team.

Eevee
Level 25
OT:Yours
ID:Yours
Tackle
Sand Attack
Growl
#138 Omanyte & #140 Kabuto

Location: Mt. Moon

Method:
The choice between the Helix and Dome fossils is given at Mt. Moon after being the top Super Nerd near the exit. When handed over at the Pokemon Lab on Cinnabar Island, a revived prehistoric Pokemon will be later available. Omanyte derives from the Helix Fossil and Kabuto from the Dome Fossil. Both are decent in their own right however Omastar has superior defence and Kabutops superior attack when it comes time for evolution.

Omanyte
Level 30
OT:Yours
ID:Yours
Water Gun
Withdraw
Kabuto
Level 30
OT:Yours
ID:Yours
Scratch
Harden
#142 Aerodactyl

Location: Pewter City

Method:
Aerodactyl must be resurrected from the Old Amber, which is found in the Pewter City museum (back entrance, requires Cut). Like the other fossil Pokemon the item must be taken to Cinnabar Island Pokemon Lab and handed to a scientist before Aerodactyl is given. Aerodactyl is a formidable Rock/Flying-type with high Attack and Speed that can tear through enemy teams with attacks like Fire Blast, Sky Attack, and Hyper Beam.

Aerodactyl
Level 30
OT:Yours
ID:Yours
Wing Attack
Agility