There is no denying that a great many oldsters do live alone and may pass several days without seeing anyone, especially during the winter. The children are grown and have lives of their own to get on with and your friends are less mobile too. Television is your constant companion, and you can talk to it, but it is at best a one way conversation.
A dog is a constant, loyal companion who will never argue about which TV show to watch and will ask for nothing more than food and a walk. A dog always has something to do and his favorite thing to do is whatever you are doing now. Dogs just want to be included - they love doing laundry and cooking dinner. They are not too keen on vacuuming; but that's OK, I bet you aren't either!
So I suppose the real question is not "should" you get a dog; but rather what kind of dog "should" you get? There is no wrong answer to this, but I suggest you give it some careful thought and seriously consider not getting a puppy unless you really like potty training.
The many other considerations include:
What is the state of your own health and where do you live?
Do you have any allergies?
Would you be happy with a 15 pound mutt in good health?
Would you benefit from a large dog that needed two walks a day?
Can you afford a dog that requires professional grooming?
Do you have the time and the patience to do some basic dog training?
What sort of physical characteristics would you like?
Would a small dog that was paper trained be a more realistic option?
Would you like a high energy clown or a cuddly couch potato?
Would you prefer a registered breed?
Sorting this out might take a while but it will give you something to do. Descriptions of most breeds are listed in Wikipedia.com and it is a good idea to read about the character traits of various breeds even if you intend to adopt a mixed breed so that you can figure out what sort of temperament would suit you best.
Once you have an idea what sort of dog you would like you can begin your search for a companion. You have two obvious choices - the local animal shelter or searching online. Dogs in animal shelters are in urgent need of alternate accommodation so at least go to see what is available. Many shelters will take your name and number and call you if a dog of your preference becomes available.
Searching online is daunting but worth the effort. There are so many dogs available for re-homing that choosing is almost a daunting task. Take your time and don't let this put you off - ask lots of questions (especially about health and why the dog needs a new home) and if feasible go and see the dog in person before making a commitment.