Why does Eevee have so many evolutions and other pokemon don't?
Excellent question, Corazon ^^
It's simply because Eevee is the genetic pokémon. Like the pokédex says: It's genetic code is irregular, so it can evolve in many different ways, depending on the circumstances and environment.
There are fish pokémon, magnet pokémon, ladybird pokémon, fire horse pokémon... and there is an evolution pokémon. That is Eevee's unique thing, to go from plain, normal-type, unbelievably cuddly creature, to strong a strong creature with speciality in a certain type.