Evolutionary Stones

An evolutionary stone causes some Pokémon to evolve.
If a Pokémon's next stage requires the use of a stone, then it can be applied at any time, thus causing instant evolution.
All Evolutionary stones can be found in many places, and are uncommonly found in the Underground of Sinnoh, unless noted otherwise.

FIRE STONE
Evolves
Vulpix → Ninetales
Growlithe → Arcanine
Eevee → Flareon

WATER STONE
Evolves
Poliwhirl → Poliwrath
Shellder → Cloyster
Staryu → Starmie
Eevee → Vaporeon
Lombre → Ludicolo

THUNDER STONE
Evolves
Pikachu → Raichu
Eevee → Jolteon

LEAF STONE
Evolves
Gloom → Vileplume
Weepinbell → Victreebel
Exeggcute → Exeggutor
Nuzleaf → Shiftry

MOON STONE
There is a very small chance of stealing a Moon Stone off of a wild Lunatone or Clefairy with Thief or Covet.
Evolves
Nidorina → Nidoqueen
Nidorino → Nidoking
Clefairy → Clefable
Jigglypuff → Wigglytuff
Skitty → Delcatty

SUN STONE
There is a very small chance of stealing one off of a wild Solrock with Thief or Covet.
Evolves
Gloom → Bellossom
Sunkern → Sunflora

SHINY STONE
One can be found on Iron Island, and another on Route 228. They are also available with the Pickup ability, or can be Mystery Gifted from Pokétopia for 7200 Poké Coupons.
Evolves
Togetic → Togekiss
Roselia → Roserade

DUSK STONE
One can be found in the Galactic Veilstone building, and another in an area of Victory Road that can only be accessed after the defeat of the Elite Four. They are also available with the Pickup ability, or can be Mystery Gifted from Pokétopia for 7200 Poké Coupons.
Evolves
Murkrow → Honchkrow
Misdreavus → Mismagius

DAWN STONE
One can be found in Mt. Coronet and another can be found on Route 225. They are also available with the Pickup ability, or can be Mystery Gifted from Pokétopia for 7200 Poké Coupons.
Evolves
Kirlia ♂ → Gallade
Snorunt ♀ → Froslass

OVAL STONE
An Oval Stone can be found in the Lost Tower. More can be found underground and there is a good 50% chance it can be held by a wild Happiny or Chansey. Unlike other stones, it is not used on the Pokémon to evolve it, but instead held by it.
Evolves
Happiny → Chansey (level up when held during the day)

EVERSTONE
An Everstone is unlike any of the other stones, as when a Pokémon holds it, they will not evolve.