I made a list of qualities that I wanted in my dog. Female, NOT a puppy, medium sized, intelligent, not hyper, etc. I then went to the pound looking for this dog. I intended to keep going back, once a week, for a year if that's what it took until I found "my" dog. I lucked out and found my baby (a Border collie mix) on the first try. She sleeps with my kids and I pity the idiot who tries to get to HER babies! ;-)
Long story short, I didn't look for a breed, I looked for characteristics.