The Eeveelutions are an interesting and versatile group of Pokémon.
Vaporeon
Vaporeon was recently moved to UU where, with it's high HP and SDef, it can serve as a pretty good wall and a great cleric.
Common Set:
Vaporeon @ Leftovers
Ability: Water Absorb
EVs: 192 HP / 252 Def / 64 SpA
Bold Nature
- Scald
- Wish
- Protect
- Heal Bell
Jolteon
Jolteon is a great choice for a RU Special Sweeper. It has great SAtk and Speed and is one of the better lower tier Electric-type Pokémon
Common Set:
Jolteon @ Life Orb
Ability: Volt Absorb
EVs: 4 HP / 252 SpA / 252 Spe
Timid Nature
- Thunderbolt
- Signal Beam
- Hidden Power [Ice]
- Volt Switch
Flareon
Flareon has been moved to the newest tier, PU! Flareon is usually used as a Guts Attacker. It serves it's purpose well and is benefitted by nice physical learnset.
Common Set:
Flareon @ Toxic Orb
Ability: Guts
EVs: 252 HP / 252 Atk / 4 SpD
Adamant Nature
- Flare Blitz
- Facade
- Superpower
- Quick Attack
Espeon
Espeon has been recently moved to UU, but it is one of the more versatile Eeveelutions; providing a great Special Sweeper, Baton Passer, and a good Pokémon to lead with seeing as it can set up both Light Screen and Reflect and uses it's ability Magic Bounce to use it's opponents status moves against it.
Common Set:
Espeon @ Focus Sash
Ability: Magic Bounce
EVs: 4 Def / 252 SpA / 252 Spe
Timid Nature
- Psychic
- Dazzling Gleam
- Hidden Power [Fire]
- Grass Knot
Umbreon
Umbreon performs a very similar role to Vaporeon and can also be found in the same tier (UU). It can still heal it's teammate and itself using Wish and can heal status conditions use Heal Bell. Umbreon has lower HP than Vaporeon, but higher Def and SDef.
Common Set:
Umbreon @ Leftovers
Ability: Synchronize
EVs: 252 HP / 4 Def / 252 SpD
Calm Nature
- Heal Bell
- Wish
- Protect
- Foul Play
Leafeon
Leafeon is a good choice for a NU Physical Sweeper. With access to Swords Dance and a high attack stat it is a powerhouse.
Common Set:
Leafeon @ Life Orb
Ability: Chlorophyll
EVs: 4 HP / 252 Atk / 252 Spe
Adamant Nature
- Swords Dance
- Leaf Blade
- Knock Off
- Return
Glaceon
Glaceon is often considered one of the least useful Eeveelutions (hence it's drop to PU) seeing as it has a limited learnset and is easily knocked out due to Ice types have so many weaknesses.
Common Set:
Glaceon @ Choice Specs
Ability: Ice Body
EVs: 252 SpA / 4 SpD / 252 Spe
Modest Nature
- Frost Breath
- Shadow Ball
- Hidden Power [Ground]
- Signal Beam
Sylveon
Sylveon is the newest addition to the Eeveelution family and the only one to remain in OU. Sylveon can also serve as a cleric and is extremely useful defensively due to Fairy types having only two weaknesses.
Common Set:
Sylveon @ Leftovers
Ability: Pixilate
EVs: 252 HP / 4 Def / 252 SpD
Calm Nature
- Hyper Voice
- Wish
- Protect
- Heal Bell
In summation:
Vaporeon can serve as a useful cleric due to it's high HP
Jolteon can be a great Special Sweeper due to it's high Speed and SAtk
Flareon is a good Guts Sweeper because of it's great Atk
Espeon can serve a variety of purposes due to it's great ability and SAtk
Umbreon can be used as a wall and cleric due to it's high defenses
Leafeon is a great Physical Sweeper, especially if you can get in a Swords Dance
Glaceon is mildly useful as a SAtker
Sylveon is another great cleric due to it's helpful typing or can serve as a SAtker
Remember, these movesets provided are mere suggestions based off of commonly used sets. It can be argued that these Pokémon can serve another purpose or use a different build, but these are the most common.