Can Eevee evolve without a stone?

yes if you make it happy in the day it evolves into espeon (without a stone) if you make it happy during the night it evolves into umbreon (without a stone)

That is true but there are other ones. They are listed below:

Flareon----- USE a fire stone on it

Glaceon----- level up on route 217 near icy rock

Leafeon----- level up in Eterna forest near moss rock

Vaporeon----- USE a water stone on it

Jolteon----- USE a thunderstone on it