When this sort of question comes up there's always those who think it's insane to get emotionally attached to things that, quite frankly, don't exist. But my reply to that is that fictional characters of all sorts are not things nature/God intended for humans to deal with. So it's to be expected that we might get attached to things that 'don't really exist'. It just all falls under the category of suspension of disbelief. To a certain extent the ability to set aside reality and willingly engage in fantasy is a sign of a healthy mind (I've head that some hardened criminals on death row are unable to do this even if they're just watching a play). Now, should someone think their Pokémon are truly alive and just trapped in their cartridges that person would have some... um, issues with reality. But no one in this thread so far has shown signs of that.
Getting attached to fictional characters = totally healthy in moderation.
So yeah, I am attached to a few of my Pokémon. My LeafGreen cartridge has been missing for two years now and I miss my Charizard terribly despite having raised another Charizard on FireRed On that game I also have a Pikachu and a Goldeen I used to beat the Elite Four because I couldn't bare to evolve them. It seems that I moved over my Bellossom from that game over to Colosseum and I was thrilled when I figured out how to clone her so I could use her in SSilver ♥ I'm more attached to Pokémon I've spent a lot of time on. I've got a Gengar I raised from a baby on his home cartridge. Took forever @_0 I like that dude LOTS.