Vaporeon. This might be a cheesy reason, but in almost every game vaporeon clears the hardest battle for me. Pokemon Rumble Blast: Couldn't beat the final level leading to Axel world(?) quit for about a month. Came back to it, and I caught a Vaporeon. IT CLEARED THE FREAKING LEVEL. Pokemon Black 2- Had a spare eevee and evolved it to Vaporeon, trained it, and all that. I was stuck on the final gym as my pokemon were underleveld (I speed by the game fast and I don't train) Vaporeon beat it for me.. Loved the thing ever since.
Umbreon all the way. I usually gravitate towards Dark types, though Ghost types are my favorite overall. Hopefully they decide to introduce a Ghost Eeveelution at some point... 7th gen perhaps?
I love the original 3 eeveelutions. The later evolutions just didn't impress me. Until Sylveon came out. Now I'm obsessed. She's just so cute! I'm currently breeding for a shiny. It's taking foreeeevvvveeeeerrrr, but it will be worth it when I have a kick-ash Pokemon. Cute and deadly.