Jolteon was my favorite for a while, but then Espeon came along and I instantly loved it. A purple psychic cat with a simple yet effective design? I'm a fan ^^
My favorite is Vaporeon. I really like this Pokemon since the first time I had it in my team in the game Pokemon XD. Also I love his look. As my second favorite, I would say Sylveon.
Jolteon.
When I have an Eevee and I'm waiting to see which type I need coverage on, it's usually always electric where I think I'm lacking (either from a shortage of wild electric types to that point, or me just being picky and not liking any of them). Jolteon more or less grew on me from this since I think I've always ended up turning Eevee into Jolteon in my first play through of a game.
I love Umbreon looks, but I've not really used it since Gold/Silver since dark type moves have become increasingly common on none dark type Pokemon, and I kinda prefer to just have that than a dedicated dark type.
I also love Glaceon's appearance but never actually had one. I just don't bother with ice types.
Flareon! Just because In Gen 1, it looked soooo fluffy and while it looks innocent and plush, it has that look that makes it look like it will set you ablaze (Bonus Points)! But that's for appearance. In terms of actual effectiveness, I would actually say Espeon or Jolteon.
I like a lot of the Eeveelutions, so it's a bit difficult to decide. My top two are probably Jolteon and Leafeon. The better of the two is probably Jolteon.
I feel like Jolteon wins out because I've used it numerous times and it's a pretty good Electric type, but I really like Grass Pokemon and Leafeon looks great.
As for the others:
Vaporeon can work a few different ways and I like its design. It's a good contender for third place.
Umbreon is pretty nice and I only came to really like it in recent years because I've abandoned my "all offense all the time" playstyle to add in things like Walls. Umbreon is fun to use now that I can appreciate it.
Glaceon and Sylveon kinda share a spot in that I like to use them but they're not all that remarkable. They're good, but I'm not crazy for them.
Flareon is gorgeous but it has a terrible moveset and it's kind of disappointing how useless it was for years. It gets Flare Blitz now, but I'm not really a fan of recoil damage if it can be avoided. Even now it's not something I'm excited to put on a team.
Espeon has a nice design but I'm let down by its movepool. I used to vastly prefer it to Umbreon but now it's maybe my least favorite.