One of the hardest questions ever! Just as hard as picking a starter! I love them all. Umbreon, Glaceon, and Jolteon I guess. I can't choose the absolute best in my opinion though, thats too difficult!
I wish I could vote for more than one option in this poll. Because I can't choose between Flareon or Leafeon. I like Flareon for its design and fire type and I like Leafeon for its design and battle capability (it doesn't look like it, but it's a tank!). xP
I enjoy training up all the Eeveelutions and then using them semi-competitively just for kicks.
In the end, I've enjoyed Jolteon the most. But Leafeon comes in right behind.
Umbreon is my least favorite, followed by Vaporeon and Glaceon. Why those three at the back? They are best-suited as stallers and or walls. I hate those types of Pokemon. I'm like Ash: all about the sweeper.
My favourite one is Umbreon since Gen 2, however if this is about competitive use then Espeon - Magic Bounce is undoubtably the best Eeveelution for me. Other than that Vaporeon and Jolteon are close seconds in the competitive realm, but Umbreon certainly does have it's great walling capabilities, which should never be underestimated.