Recently a well meaning friend rescued a young cat from certain death on a very busy road in Maryland only to find out later that the cat was put down by the shelter he brought her to. Obviously he was very upset but didn't know that all shelters have different policies.
Your local Animal Control is usually considered to be a high-kill shelter. When an animal is turned in to them or picked up by them, they only hold the animal so many days before they are euthanized. Other animal shelters follow this policy as well, only keeping cats and dogs that are healthy, well behaved and easily adoptable. All others are euthanized. Feral cats and stray dogs are of questionable back grounds will usually be euthanized in high-kill shelters and that is unfortunately was what happened to my friend's rescued cat.
Other animal shelter are considered to be low-kill shelters, meaning they will put down cats or dogs that have serious health issues, are injured or test positive for chronic diseases like Feline Leukemia or if they have serious behavior issues.
The best option would be a no-kill shelter. These shelters will go great lengths to get medical treatment, correct behavior issues - anything it takes to spare the life of a cat or dog brought in to them. Or they will find another shelter that can deal with whatever issue the pet has and then find a forever home for them.
A very serious note about euthanasia - shelters vary on their means of putting the animals down. Many use lethal injection - the most humane way to euthanize but many shelters still use the gas chamber which is a very stressful, horrible way to die. There are other even more barbaric forms of euthanasia used in shelters, so again - be sure you know what form of euthanasia the shelter using or take the animal to a no-kill shelter - the best way to go! Do not be mislead by the misnomer Humane Society Shelter - their policies may be anything but humane!
Helping a stray dog or cat is a wonderful thing to do but please make sure you know the policies of the shelter you are surrendering them to - it could mean the life of that very animal you wanted to rescue!