Eevee had three evolutions in the first-generation Pokémon games: Vaporeon, Jolteon, and Flareon. These three forms appeared alongside Eevee in Pokémon Red and Blue and represented Water, Electric, and Fire types.
Eevee’s unstable genetic code is the fictional explanation for its branching evolution paths. Players could use a Water Stone, Thunder Stone, or Fire Stone to evolve Eevee into the corresponding form. This made Eevee different from most Pokémon, which generally had a single evolutionary route.
Eevee now has eight total evolutionary forms, so the answer depends on the historical scope of the question. Espeon and Umbreon arrived in the second generation, followed later by Leafeon, Glaceon, and Sylveon. The first-generation count is therefore three, not the modern total of eight.