I get attached to my team Pokemon. I fight with them through many tough battles, so it's only natural. I remember back when I was a young child playing Blue version and my data got lost. I cried so hard, I was so attached to them.
But seeing as Jigglypuff is my favorite Pokemon, I have a Jigglypuff that I'm really attached to. When I was getting back into Pokemon, I bought a copy of Emerald, and remembering my fondness for the puff, went looking for one. Ran into a male Jigglypuff, caught it immediately with one throw of a Premier Ball.
It's now at level 100, with 38 ribbons. It's pretty much my dearest Pokemon; every time I get a new game, I trade it over to get whatever awards a Pokemon can get with it. And just like Some_Chick is a crazy Absol breeder, I'm a crazy Igglybuff breeder. The children of my prized Jigglypuff have traded for many good Pokemon, although I give them away just to spread the Puff Love.