We had several different dogs when I was a kid and all but one of them were older rescue dogs that we got from the pound.
Like others say the great part of it is that most of them are already housebroken and you know what you are getting so you don't do like a friend of mine and get a puppy that you think is going to grow up to be about a 30-40 pound dog and end up with a 110 pounds beast
I would highly encourage you to do it. Just make sure to ask if the dog has had any shots and if they know about any medical issues the dog has. Otherwise, just spend a little time with the dog, take it out in the parking lot by the building and walk with it, try to see what kind of personality it has and what its energy level is and if you can work with that.
Also ask about the situation the dog came from. If it was badly abused and you have kids it might not be a good dog to have around because it might spook easy and nip. You will find a lot of those dogs are simply dogs that people no longer can care for so they dump them at the pound.