Most of my horses have been mutts. A couple have been registered - one QH and one APHA, but the vast majority were mutts.
My heart horse was a QH, but unregistered. I bought her at an auction without even riding her. I had watched a couple of teenage girls riding her double, and she was weaving in and out of traffic in the parking lot without turning a hair. I figured if the price was right, I'd give her a go. Got her for $250, and it turned out to be the best $250 I'd ever spent.
My current horse is also a mutt, most likely. She's shaping up to be as good a horse as my old mare was, to our surprise. I bought her sight unseen, the very day after I chewed a friend out for buying horses from other breeders across the country without really knowing the first thing about them. Had to eat my words, didn't I?