Well, of our lifetime, I'd say 3 we picked and 3 the fates-that-be picked for us. The first three cats we had, two we chose from the breeders (*cough*BYB*cough*) and one we chose from the shelter. The next three (Willow, Buffy, Molly) came to us by their own will. Well, technically we "picked" Willow, but I'm not sure that's right, because of the whole litter, only one wasn't a dilute tortoiseshell (he was an orange-and-white). It was just a pack of sleeping, dead-to-the-world dilute torti kittens. I think we just went eeny-meeny-miney-mo and ended up with Willow. But Buffy came when my brother's girlfriend at the time, who worked at a vet clinic, came over with an orphaned kitten she thought we'd like to meet, and Molly came to us in the guise of a kitten stuck in a tree and lost from her owners (nobody ever called for her)
The first three kitties we had, who we picked ourselves, went as follows:
Yoshi - he was the last surviving member of his litter (disgustingly, his breeder, an aging woman, gassed the litter to death, though I'm not sure why she spared Yoshi). Yoshi was also born with a problem with his back legs, where they didn't work as they should, but he grew out of it and was a completely normally kitten by the time he came to live with us
Sasha - we picked him out at the shelter after Yoshi "ran away" (hah, yeah right. Poor guy was probably hit by a car). My brother picked him out, so I guess we got Yoshi because he was "cool" (I guess young boys don't care for kittens, they like the full-grown, long-haired fluffy MEN, lol)
Grizzly - we chose him ourselves, but there were two kittens ahead of him. First one, by my own choice, was a shorthaired grey female, but my family said no (totally sexist, dad didn't want any females; too "scratchy" and "crazy," apparantly). Next, I wanted a longhair black-and-white like Yoshi had been, but that one was already spoken for by the breeders' relative (the "breeders" were one of our neighbours and one of the kids was my good friend). So we chose the longhair black guy, and he ended being a delight.