In late 2006, a video appeared on YouTube demonstrating how to beat the classic Pokémon game in about 7 minutes. This technique can be done on an actual GameBoy and does not require extreme luck or reflexes. However, it works only on Pocket Monsters Red (v1.0) (J) and Pocket Monsters Green (v1.0) (J), the first versions of the game that came out in Japan in 1995.
To explain this route in detail would require many screenshots, so instead I have just embedded the YouTube video on this page.
The following description was originally written by gocha. I have added details where appropriate.
1. Start the game.
2. Obtain two items, きずぐすり (potion) and おとどけもの (Oak's parcel).
3. Open どうぐ (item screen), then point the second item and press Select, B, B.
4. Encounter with a wild pokémon, then open ポケモン (PKMN) screen and press A (selected pokémon will be garbled).
5. Cancel PKMN screen and beat the wild pokémon.
6. Walk in circles for N steps (and stand in front of Gary's house), and enter the house (to emulate the original video, N=83~87).
7. Ash warps to to the area east of Celadon City. Walk into the guardhouse, then out.
9. Take a direct walk into the Pokémon Center of Celadon City, then out.
10. Walk into the entrance four buildings to the left of the Pokémon Center, then out.
11. Move toward the Pokémart, then walk back and forth for 18 steps, then enter the building.
12. Ash warps to Lance's room. Go up to Gary's room.
13. Walk past Gary to meet Professor Oak.
The above route may be the most basic method which you should be able to reproduce. Nonetheless, this route has been improved upon several times by speedrunners (both conventional and tool-assisted). On YouTube, you may find some of the newer videos that beat the game in less than 5 minutes.