Eight Gym Badges are needed to enter the Indigo Plateau in Pokémon Red and Blue.
In the Kanto storyline, a Trainer must defeat eight Gym Leaders and collect their Badges before the game allows access to Victory Road and the Pokémon League at Indigo Plateau. Each Badge also permits the use of particular field moves outside battle.
The eight Kanto Gyms are associated with Pewter, Cerulean, Vermilion, Celadon, Fuchsia, Saffron, Cinnabar, and Viridian. The exact order of some challenges can vary, but all eight Badges are required for the League journey.
The Indigo Plateau is not itself a Gym. It is the Pokémon League complex where the player battles the Elite Four and the Champion. Other Pokémon regions also generally use an eight-Badge structure, which can cause details from different games to be mixed together.