A lot of people feel that an adult dog (out of puppy-hood) is a better pet for them. Older dogs don't require as much attention as a growing puppy does. They are often easier to housetrain (if not already) because they can hold their eliminating for longer periods of time. They are past the chewing stage, and have settled down from the boisterous adolescent behavior.
Also, with an adult dog you have a much better idea of what you are going to end up with. Adult dogs present no surprises in their final size and appearance.
When an adult dog is put into a new situation, they are looking for leadership and will attach to you almost immediately. Even breeds known as "one-person" dogs will accept a new master rather easily. For example, observe the relationship between a blind person and a German Shepherd guide dog. These dogs have been through at least three homes before they're finally matched up with ther blind companions.