Vaporeon is my absolute favourite, and has been since playing Red.
I've never been a fan of water pokemon. When playing through Red I just never seemed to find one I liked, especially with them being harder to come by in the beginning due to needing a rod. I can't say I'm keen on fish-based Pokemon, and Pokemon like Krabby and Seel just don't appeal to me. Vaporeon stood out by being a critter I liked the look of, and being a strong water-type. Funnily enough I actually really wanted Jolteon, but as I already had Pikachu on my team and I disliked all the other water Pokemon I'd encountered, it just made sense to use that Water Stone.
Which leads me to my second favourite, Jolteon. Love the design. So much. I loved his little cute voice in the anime. He's one of the those Pokemon that I really loved, but never got round to training until FireRed, where I had a Vaporeon and a Jolteon. I may raise one for competitive battle one day, but as I already have Manectric and a Vaporeon on my Team, he's either pointless or breaking the rules with species clause.
As for the others, I like them. Leafeon and Glaceon are a bit 'meh' to me, but as I've never trained them I don't have much to say.