Pokemon Gold and Silver introduced more one-shot Pokemon than Red and Blue did. Like with the legendary Pokémon, there are a variety of Pokémon who are available by interacting with them on the map, though these Pokemon can be bred. The methods listed here are the only way you can capture these special Pokemon in Gold and Silver.

#101 Electrode

Location: Mahogany Town Rocket Hideout

Method:
The Mahogany Town Team Rocket base uses three Electrodes to power the radio transmitter. In order to turn it off, you must defeat or capture them. They shouldn't be too much trouble (even Mud-Slap may suffice in dealing damage to them).

Electrode
Level 23
OT:Yours
ID:Yours
Hold Item:
None
Screech
Sonicboom
Selfdestruct
Rollout
#130 Gyarados

Location: Lake of Rage

Method:
Part of the Team Rocket storyline involves you facing off against a Level 30 Gyarados at the Lake of Rage. However, this isn't any ordinary Gyarados: this one is a shiny red colour, which is otherwise very hard to find. This Gyarados has superior stats to a normal Gyarados and is an excellent addition to any team. Watch for its Dragon Rage and Thrash attacks, both of which cause severe damage.

Gyarados
Level 30
OT:Yours
ID:Yours
Hold Item:
None
Tackle
Bite
Dragon Rage
Leer
#131 Lapras

Location: Union Cave

Method:
Every Friday you can find Lapras in the basement of Union Cave. It is still an excellent Water/Ice-type and is highly recommended. Lapras might be hard to catch so it is recommended you use status moves and the specialty balls like Heavy Balls or Level Balls.

Lapras
Level 20
OT:Yours
ID:Yours
Hold Item:
None
Growl
Slam
Mist
Body Slam
#143 Snorlax

Location: Vermilion City

Method:
This incredibly lazy Pokemon blocks the path to Diglett's Cave in Vermilion City and requires the EXPN Card from Lavender Town to wake up. This can be obtained by retrieving the stolen Machine Part from Cerulean City Pokemon Gym and bringing it to the Power Plant on Route 10 to jump start the generator. Snorlax is very strong and has high defenses so be careful. Heavy Balls are definitely recommended for this catch.

Snorlax
Level 50
OT:Yours
ID:Yours
Hold Item:
None
Rest
Snore
Body Slam
Rollout
#185 Sudowoodo

Location: Route 36

Method:
Sudowoodo, like Snorlax in the first generation, blocks the path to another part of the region. In this case, Goldenrod City and Ecruteak City are both cut off from Violet City due to its interference. It can be moved only by the use of a Squirtbottle obtained in Goldenrod City (which requires a detour through Union Cave and Ilex Forest to get to) after defeating Whitney. The Level 20 Rock-type has a few good moves and is tricky to catch but may be worth it if you're looking for a Pokemon with high Attack and Defense early on in the game. It has modest Special Defense but is very slow so be careful if you do use it in battle.

Sudowoodo
Level 20
OT:Yours
ID:Yours
Hold Item:
None
Rock Throw
Mimic
Flail
Low Kick