Every cat and dog we've had over the last 40 years have all been "rescues". Except for a young and fairly sickly feral kitten that adopted us, all the ones we've gotten from veterinarian's offices or shelters have been wonderful pets.
Same here and I have not regretted it one time. I actually think those critters know you saved them and are more affectionate and well behaved. I also still think Mutts are the smartest breed of any species!
When I was a kid growing up on the farm, a local fertilize/tankage company maintained a barn out in the middle of nowhere where you could bring dead livestock and drop them off. The smell was incredible. I would hold my breath from the time I got out of the truck till the time I got back in. I remember seeing piles of dead dogs and cats from the local humane society/animal pound that never got adopted and were put down. Ever since, I have always gotten my pets from the humane society and had every last one of them spayed or neutered!