I'm a Glaceon gal, the ice Eevee won me over in Battle Revolution of all games, proving to be reliable and powerful. She never went down before KOing a foe first. Plus, Glaceon has a really elegant design, which I find appealing. And, of course, despite all its shortcomings, ice is one of my preferred types, which also helps.
I have to give a shout-out to Boweon, the fairy Eevee I once found repulsive. Using one in X turned my opinion right around, and I eventually grow fond of the "girly" design. Leafeon also gets special mention, I can't exactly put my finger on why, but I have quite the soft spot for the verdant Pokémon. And Espeon, because it looks like a cat. And...
I'd better stop now. Needless to say, the Eevee family ranks among my favourite Pokémon, and they've all left their mark on me for one reason or another cx