I volunteer for a no-kill shelter, and when I started I was surprised to learn a few things. First, (in Chicago at least, but probably in other cities) the city pound is required to hold onto strays for 5 days. Owner relinquishments have no hold requirement. Therefore, if you drop your dog or cat off at the pound and the pound is full of strays and there isn't room for your pet, it used to be that your pet would be put down within a few hours. With the decrease in strays in the city (mostly due to an increase in spaying/neutering), the rate at which animals are euthanized has been slowed and more of them have a chance to be rescued. My particular shelter sends someone to the pound once a day to survey the animals who are waiting to be euthanized and select a certain number to bring back to our intake center (and once they're there, we only put animals down for severe health or severe behavior issues). Other rescues— breed-specific rescues, foster networks, low-kill shelters— visit the pound and scoop up animals as well. Some city pounds are also becomming more progressive about releasing certain abused animals to adopted homes. In the past, abused animals were held as evidence in animal cruelty cases and after the case were usually euthanized. I've seen probably half a dozen cruelty cases come through the shelter, and all of them have been adopted.

Anyway, the point of this long post was that it's horrible that so many pets are euthanized every year, but it's getting better. And adopt your next pet. Even if you have your heart set on a purebred, shelters get purebred dogs all the time.