In my profession, this particular issue is two-pronged. There is the pet owners viewpoint where they want to let their four-legged friend have some freedom to run and play. But there is also the question I am asked when dealing with service dogs in regards to the legality of a leashed animal. I am going to address the service dog aspect in this particular discussion, but some of this information can be used across the spectrum of dog handling.
According to the ADA, this is the legal statute for dog handling:
(d) Animal under handler’s control. A service animal shall be under the control of its handler. A service animal shall have a harness, leash, or other tether, unless either the handler is unable because of a disability to use a harness, leash, or other tether, or the use of a harness, leash, or other tether would interfere with the service animal’s safe, effective performance of work or tasks, in which case the service animal must be otherwise under the handler’s control (e.g., voice control, signals, or other effective means).
Basically, the dog MUST be under control, preferably by means of a harness, leash or tether but if that is not possible some other means is required.
I believe in having a dog secured at all times for the safety and protection of the dog and its handler. When taking any dog for a walk, you must always keep in mind the environment you are going into and you should not assume you or your dog will be able to control natural elements around you. You could encounter a stray dog that has not been in the neighborhood before, and before you know it there is an injury. A leash can keep your dog next to you while you turn away from the threat, it can be used as a weapon if necessary as well. It can help you keep your dog under control and sometimes that is enough to diffuse a situation before it gets too volatile.
It is impolite to have your dog just run up on other people. Even if the other person is a dog lover, that is no reason for your dog to announce itself in such an unruly and intrusive manner. Remember, cute and fun behavior in your eyes is not always seen as that from others. A little respect by keeping your dog on-leash and controlling how it interacts with others shows thoughtfulness, consideration and awareness. Also, a true, properly trained service dog will never behave in this fashion which is a great distinguishing factor from the dog being someones pet or a service animal.
So, to wrap things up in that pretty little package, if you have a pet please be courteous to others and keep your dog under control at all times. There are states/cities where this is the law. If it is a service animal the federal law requires that you do so. It is best for all involved if you do.